10
10
Savings
and investments
FINANCIAL MATHEMATICS
As our economy grows and our standard of living improves, Australians are becoming more informed about financial planning and investing their money wisely. People once kept all of their savings in banks, but today investors will also look elsewhere for higher interest rates and better returns for their money. For example, half of adult Australians now invest in the stock market and own shares, especially since well-known companies like Telstra and Woolworths put out their public float offers.
This chapter is about the mathematics of saving and investing money, in financial institutions, in the stock market and in items that appreciate in value. It examines the calculations, terminology, graphs and tables involved in managing investment accounts and share portfolios. The formulas and relationships involved with simple and compound interest are also analysed.
In this chapter you will learn how to:
calculate simple and compound interest using appropriate formulas
construct and examine tables and graphs involving simple and compound interest
calculate fees and charges associated with savings and investment accounts
understand and use the language of the stock market
calculate the costs involved in buying and selling shares
calculate dividends and dividend yield from shares
read and interpret tables and graphs depicting share prices
SIMPLE INTEREST
Interest is money earned from an investment with a bank, credit union or other financial
institution. The original amount of money invested is called the principal, and simple
interest occurs when the interest is calculated as a percentage of this principal. Simple
interest is found by multiplying the principal by the percentage interest rate, then multiplying this result by the term of the investment (the number of months or years):
Simple interest = principal × interest rate × term
So simple interest is directly proportional to the principal, unlike compound interest, which varies as the value of the investment increases. Another name for simple interest is flat rate interest.
Simple interest is represented algebraically by the following formula:
Example 1
A sum of $14 510 is invested at 10.25% p.a. for 8 months. Calculate the simple interest earned.
Solution
Because the interest rate r is expressed per year, the number of periods n must also be expressed in years.
P = $14 510, r = 10.25% = 0.1025, n = years
I = Prn
= $14 510 × 0.1025 ×
= $991.5166 …
≈ $991.51
When calculating earned interest to the nearest cent, round down. Financial institutions cannot round up, otherwise they will be paying each investor an extra part of a cent.
Example 2
Calculate the simple interest earned on $1840 invested at 1.06% per month for 1 years.
Solution
P = $1840, r = 1.06% = 0.0106, n = 1.5 × 12 = 18 months
I = Prn
= $1840 × 0.0106 × 18
= $351.072
≈ $351.07
I = Prn where P is the principal (initial value),
r is the interest rate per period expressed as a decimal, and n is the number of periods in the term.
8 12
---8 12
---1 2
---n is expressed i---n mo---nths because the
Example 3
What was the interest rate per annum if $2800 invested for 4 years earned $1102.50?
Solution
P = $2800, n = 4 years, I = $1102.50
I = Prn
$1102.50 = $2800 × r × 4
= $12 600r
r=
= 0.0875 The interest rate was 8.75% p.a.
Alternative method
Interest for 4 years= $1102.50
Interest for 1 year=
= $245
∴ Interest rate p.a.= × 100%
= 8.75%
1. Calculate the simple interest earned from the following investments.
(a) $7400 at 5% p.a. for 4 years (b) $2136 at 6% p.a. for 2 years (c) $16 200 at 7.65% p.a. for 3 years (d) $4500 at 8.2% p.a. for 8 months
(e) $12 874 at 0.61% per month for 6 months (f) $5946 at 0.32% per month for 4 years (g) $4510 at 0.0301% per day for 31 days (h) $9500 at 0.0627% per day for 74 days (i) $20 016 at 7 % p.a. for 5 months
(j) $8250 at 10.5% p.a. for 240 days
2. Kalena earned $262.44 in simple interest from investing an amount for 3 years at
5.4% p.a. What was the amount?
3. Alan earned $5409.25 simple interest from an investment of $9835 over 5 years.
What was the interest rate per annum?
4. For how long must a principal of $15 750 be invested at 9.8% p.a. for it to earn $3087 in
simple interest?
5. Zoran earned $675 interest from $7500 invested for 9 months. What was the interest rate
per annum?
6. What principal would earn $3729.60 in interest if invested for 3 years at 16.8% p.a.?
1 2 ---1 2 ---1 2 ---$1102.50 $12 600 ---1 2 ---$1102.50 4.5 ---$245 $2800
---Exercise 10-01:
Simple interest
---7. OzExpress Credit Union has the following term deposit accounts, where the principal
must be invested for a fixed period.
Calculate the simple interest earned on the following investments.
(a) $6300 for 3 years (b) $13 750 for 8 months
(c) $7800 for 5 years (d) $14 240 for 2 months
(e) $5000 for 4 years
8. Kylie earned $80.58 interest from an investment of $2530 over 91 days. What was the
interest rate per day (correct to 2 significant figures)?
9. For how long would $4720 need to be invested at 0.67% per month to earn $474.36 in
simple interest?
10. An amount of $9020 was invested for 2 years and earned $1731.84 in simple interest.
Calculate the monthly interest rate.
11. Terry earned $1980 in interest from an investment with a term of 4 years at 3% per
half-year. What was the value of his investment?
12. Maxine invested $5660 in an account and earned $636.75 in interest after 15 months.
What was the interest rate per quarter?
Visit your local bank or credit union and collect information about the different types of saving accounts available, including the interest rates and conditions imposed on each.
Examples: savings account, investment
account, fixed term deposits, cheque account, Christmas club account, young saver account, deluxe account, incentive saver account.
Current interest rates can also be found in the financial pages of daily newspapers or on the Internet.
1. In which type of account would you
choose to save?
2. Compare and contrast the different types
of account and compile your findings in a report.
Term Interest rate
1–6 months 8.75% p.a.
7–11 months 9.25% p.a.
1–3 years 10.5% p.a.
4–5 years 12% p.a.
Minimum investment $1000
COMPOUND INTEREST
In reality, calculating interest is not so ‘simple’ and straightforward. Simple interest is used only when the interest earned is collected by the investor and not added to the investment, such as in a term deposit account. With most accounts, however, the balance plus the interest becomes the new balance on which the interest is calculated next time. In other words, the interest will increase because you also earn ‘interest on your interest’. This is called
compound interest. Compound means ‘to combine’.
Example 4
If a principal of $3000 is invested at 6% p.a. interest, compounded over 3 years, what is: (a) the value of the investment after 3 years?
(b) the compound interest earned?
Solution
(a) After the 1st year, Interest = $3000 × 0.06
Amount of investment= old principal + interest
= $3000 + ($3000 × 0.06)
= $3000(1 + 0.06)
= $3000(1.06) After the 2nd year,
Amount of investment= $3000(1.06) + interest
= $3000(1.06) × 1.06
= $3000(1.06)2
After the 3rd year,
Amount of investment= $3000(1.06)2+ interest
= $3000(1.06)2× 1.06
= $3000(1.06)3
= $3573.048
≈ $3573.04
Notice from the pattern that the principal $3000 is being increased by the interest rate 0.06 successively 3 times, where 3 is the number of years. Generally, this can be summarised by the formula A = P(1 + r)n, where P is the principal, r is the decimal
interest rate, n is the number of periods, and A is the final amount of the investment. (b) The compound interest earned after 3 years is simply found by subtracting the original
principal from the final amount of the investment. Compound interest earned= $3573.04 − $3000
= $573.04
Rounding down to the nearest cent
Adding 6% interest to the principal is equivalent to increasing the principal by 6%
Increasing $3000(1.06) by another 6%
Increasing $3000(1.06)2
by another 6% Rounding down to the nearest cent
The compound interest formulas are
A = P(1 + r)n and I = A − P where A is the final amount,
I is the compound interest, P is the principal,
Example 5
Calculate the final amount and compound interest earned when $3200 is invested at 8.5% p.a. for 4 years.
Solution
P = $3200, r = 8.5% = 0.085, n = 4
A = P(1 + r)n
= $3200(1 + 0.085)4
= $3200(1.085)4
= $4434.7478 …
≈ $4434.74 The final amount is $4434.74.
I = A − P
= $4434.74 − $3200
= $1234.74
The compound interest earned is $1234.74.
Example 6
If $12 500 is invested at 4.8% p.a. with the interest compounded monthly, calculate the final balance and total interest earned over 2 years.
Solution
As interest is compounded monthly, r and n must be expressed in months:
P = $12 500, r = % = 0.4% = 0.004, n = 2 × 12 = 24 Final balance= $12 500(1 + 0.004)24
= $12 500(1.004)24
= $13 756.8537 …
≈ $13 756.85
Compound interest = $13 756.85 − $12 500
= $1256.85
Example 7
What principal must be invested at 4.5% p.a. for 8 years so that it grows to $10 000?
Solution
A = $10 000, r = 4.5% = 0.045, n = 8
A= P(1 + r)n
$10 000= P(1 + 0.045)8
= P(1.045)8
P =
= $7031.8512 …
≈ $7031.86 A principal of $7031.86 is needed.
4.8 12
---$10 000 1.045
( )8
Many graphics calculators, financial calculators and spreadsheet software have financial modes for calculating simple interest, compound interest and final values of investments. Graphics calculators have a TVM mode that stands for time-value-money, while spreadsheets have special financial functions.
In the financial world, the compound interest formula A = P(1 + r)n is written
FV = PV(1 + r)n
where FV stands for future value and PV stands for present value (principal).
Investigate the interest calculation functions on your graphics calculator or spreadsheet.
1. Calculate the final amount of each of the following investments and hence the compound
interest earned.
(a) $7400 at 5% p.a. for 4 years (b) $2840 at 6.5% p.a. for 5 years (c) $4500 at 4.9% p.a. for 2 years
(d) $17 000 at 0.5% per month for 10 months (e) $9250 at 0.82% per month for 6 months
(f) $9000 at 8.4% p.a. for 8 months, compounded monthly (g) $12 900 at 10.8% p.a. for 1 year, compounded monthly (h) $13 800 at 7.5% p.a. for 2 years, compounded half-yearly (i) $13 800 at 7.5% p.a. for 2 years, compounded quarterly (j) $6920 at 9% p.a. for 240 days, compounded daily
2. Paul wants to invest some money so that it will grow to $24 000 in 5 years’ time, when
he will travel through Europe. If the interest rate is 5.5% p.a., what amount should he invest, to the nearest cent?
3. A sum of $8500 is invested at 7% p.a. for 5 years.
(a) Calculate the total interest earned if it is:
(i) calculated at a flat rate (simple interest) (ii) compounded yearly (b) Which type of interest is greater: simple or compound? By how much? (c) Why is one type of interest greater than the other?
4. A principal of $21 000 is invested at 5% p.a. Calculate the value of the investment after
2 years if the interest is compounded:
(a) yearly (b) half-yearly (c) quarterly (d) monthly (e) daily
5. Judging by your results from question 4, what happens to the amount of interest earned
as the frequency of compounding increases? Why?
6. Zara has $4000 in an account earning 4% p.a. interest, compounded yearly. By guessing
and checking, determine how long it will take her to double her money. Answer to the nearest year.
7. How long will an investment of $2400 take to grow to $3265 at 8% p.a. interest
compounded yearly (to the nearest year)?
8. After 8 years, the value of Corrina’s investment grew to $6260.14. What was the initial
amount of her investment if the interest rate was 8.75% p.a.?
Technology:
Interest on graphics calculators and spreadsheets
Exercise 10-02:
Compound interest
9. Determine the sum to be deposited if $10 000 is required in 6 years’ time and terms of
3.75% p.a. (compounded quarterly) are available.
10. A principal of $10 000 is to be invested for 3 years. Determine which is the best
investment option:
A. 6% p.a. simple interest B. 5.9% p.a. compounded annually C. 5.85% p.a. compounded half-yearly D. 5% p.a. compounded monthly
11. An investment of $13 500 earns 7.3% p.a. compounded half-yearly for 4 years.
(a) Calculate the interest earned and the equivalent flat (simple) interest rate per annum. (b) Does this flat rate change if the principal is different?
1. Compare the growth of an investment over 20 years under simple and compound
interest. Create a spreadsheet that allows you to enter a principal and interest rate (% p.a.) and then calculates the interest and value of the investment at the end of each year, from the 1st to the 20th year.
2. Draw graphs illustrating the growth of an investment under simple and compound
interest, using graph paper, the spreadsheet’s graphing function, a graphics calculator or computer graphing software.
1. Use the spreadsheet above to determine how long it will take to double an investment of
$8000 if invested at 7% p.a. compound interest. Answer to the nearest year.
2. Investigate whether this period changes if the principal changes.
3. Investigate whether this period is halved if the interest rate is doubled, and vice-versa.
4. Financial experts say that a law of seventies exists for finding when an original
investment will be doubled. They claim that when the product of the percentage interest rate and the number of periods is around 70, the original investment will be doubled— for example, when r = 14% and n = 5. Investigate this claim.
A B C D E
1 Principal $1000
2 Interest rate (% pa) 4
3
4 SIMPLE INTEREST COMPOUND INTEREST
5 Year Interest Investment Interest Investment
6 1 $40 $1040 $40.00 $1040.00
7 2 $40 $1080 $41.60 $1081.60
8 3 $40 $1120 $43.26 $1124.86
9 4 $40 $1160 $44.99 $1169.85
: : : : : :
: : : : : :
24 19 $40 $1760 $81.03 $2106.85
25 20 $40 $1800 $84.27 $2191.12
26 Total $800 Total $1191.12
Spreadsheet activity:
Simple vs compound interest
INTEREST TABLES AND GRAPHS
Example 8
Simple interest
Rachel invests $2000 in an account that earns 6% p.a. simple interest. Construct a graph that shows the simple interest I earned in dollars over n years, for values of n from 0 to 8. (a) What does the gradient of this graph represent?
(b) Use the graph to estimate the simple interest earned after 4 years.
Solution
I = Prn
= 2000 × 0.06 × n
= 120n
I = 120n is a linear function. Its graph is a straight line of the form y = mx + b with gradient 120 and vertical intercept 0. This line passes through the origin, so simple interest is an example of direct linear variation; that is, the interest I is directly proportional to the number of years n. To help us graph the line, we can complete a small table of values for I = 120n.
(a) The gradient, 120, is the interest earned per year ($120). (b) Reading from the graph, when n = 4 , I = $540.
n (years) 0 2 8
I ($) 0 240 960
1 2
---Interest,
I ($)
Term, n (years)
1 2 3 4 5 6 7 8 9
1000
900
800
700
600
500
400
300
200
100
(8, 960)
(2, 240)
(b)
Simple interest earned from an investment of $2000 at 6% p.a.
0
---Example 9
Compound interest
Ross invests $2000 in an account that earns 8% p.a. compound interest. Construct a graph that shows the amount A in dollars of the investment, over n years for values of n from 0 to 10.
Solution
A = P(1 + r)n
= 2000(1 + 0.08)n
= 2000(1.08)n
This is not a linear function because n appears in the power or index of the formula. In fact, this is called an exponential function, and the exponential graph is an increasing curve. We can use a table of values where A is expressed to the nearest whole dollar.
Note that the curve grows steeper than a straight line graph, illustrating that an investment grows faster with compound interest than with simple interest.
n (years) 0 1 2 3 4 5 6 7 8 9 10
A ($) 2000 2160 2333 2519 2721 2939 3174 3428 3702 3998 4318
Amount,
A
($)
Term, n (years)
1 2 3 4 5 6 7 8 9
3800
3600
3400
3200
3000
2800
2600
2400
2200
2000 4000
Amount of an investment of $2000 at 8% p.a. compound interest
10 4200
4400
Example 10
Financial tables
Before calculators became widely available, accountants used financial tables like the one below to calculate compound interest. This table is also useful when your calculator does not have a power key. It lists the value of (1 + r)n to 3 decimal places for different values
of r and n, so that you can calculate the final amount of an investment (per dollar) undergoing compound interest.
Use the table to calculate the final amount of: (a) $2000 invested at 8% p.a. for 5 years
(b) $11 000 invested at 15% per month for 8 months
(c) $4780 invested at 12% p.a. for 10 months, compounded monthly
Solution
(a) A= $2000(1.08)5
= $2000 × 1.469
= $2938
(b) A= $11 000(1.15)8
= $11 000 × 3.059
= $33 649 (c) A= $4780(1.01)10
= $4780 × 1.105
= $5281.90
COMPOUND INTEREST TABLE (1 + r)n
FINAL AMOUNT OF INVESTMENT (PER DOLLAR)
Interest rate per compounding period (r)
No. of periods (n)
0.01 1%
0.05 5%
0.08 8%
0.1 10%
0.15 15%
0.2 20%
1 1.010 1.050 1.080 1.100 1.150 1.200
2 1.020 1.103 1.166 1.210 1.323 1.440
3 1.030 1.158 1.260 1.331 1.521 1.728
4 1.041 1.216 1.360 1.464 1.749 2.074
5 1.051 1.276 1.469 1.611 2.011 2.488
6 1.062 1.340 1.587 1.772 2.313 2.986
7 1.072 1.407 1.714 1.949 2.660 3.583
8 1.083 1.477 1.851 2.144 3.059 4.300
9 1.094 1.551 1.999 2.358 3.518 5.160
10 1.105 1.629 2.159 2.594 4.046 6.192 xy
From the table: r = 0.08, n = 5
From the table: r = 0.15, n = 8
12% p.a. =12 = 1% per month
12
Equipment: Computer and spreadsheet software, graphics calculator or graphing software
1. Create a spreadsheet that reproduces the compound interest table on page 379
(Example 10), or modify it so that it calculates values of (1 + r)n for any value of r that
you enter.
2. Use a graphics calculator, spreadsheet or graphing software to construct graphs that
show simple interest or the growth of an investment under simple and compound interest.
3. Use a graphics calculator, spreadsheet or graphing software to graph on the same axes
the value of an investment of $5000 over 10 years at 9% p.a., compounded:
(a) yearly (b) half-yearly (c) monthly
1. Use the simple interest graph on page 377 (Example 8) to estimate the interest earned
when $2000 are invested at 6% p.a. for:
(a) 9 years (b) 2.5 years
(c) 6.5 years (d) 4.5 years
2. Graph on the same axes the simple interest I earned when $4000 are invested in an
account earning:
(a) 4% p.a. (b) 12% p.a.
over n years, for values of n from 0 to 10.
3. (a) Use the graph from question 2 to estimate the simple interest earned from an
investment of $4000 over 6 years:
(i) at 4% p.a. (ii) at 12% p.a.
(b) How do the two different interest rates appear on the graphs?
4. Use the compound interest graph on page 378 (Example 9) to estimate the final value of
an investment of $2000 earning 8% p.a. interest after:
(a) 9 years (b) 2.5 years
(c) 6.5 years (d) 4.5 years
5. Use the compound interest graph on page 378 (Example 9) to estimate when the
investment will reach the following amounts. Answer to the nearest year.
(a) $2500 (b) $3500
6. Graph on the same axes the amount A of a $5000 investment earning compound interest
at a rate of:
(a) 4% p.a. (b) 12% p.a.
over n years, for values of n from 0 to 10.
7. (a) Use the graph from question 6 to estimate the value of an investment of $5000 after
7 years:
(i) at 4% p.a. (ii) at 12% p.a.
(b) How are the two different interest rates indicated on the graphs?
Technology:
Interest tables and graphs
8. Use the compound interest table on page 379 (Example 10) to calculate the final value
of the following investments.
9. Use the same compound interest table to find how long will it take a principal to double
its value if it is invested at 15% p.a. compound interest (to the nearest year)?
1. Create a spreadsheet that will allow you to enter a principal, an interest rate in percentage
per annum, and a term in years, then calculate: (a) the total simple interest earned
(b) the total compound interest earned if the interest is compounded:
(i) yearly (ii) half-yearly (iii) quarterly (iv) monthly (v) daily taking 1 year as 365.25 days.
2. Banks once calculated interest on savings accounts monthly but computer technology
now allows them to calculate this interest daily. Is this better for the investor?
Principal Interest rate Period
(a) $16 000 10% p.a. 4 years
(b) $3 185 20% p.a. 8 years
(c) $1 15% p.a. 10 years
(d) $8 790 8% p.a. 2 years
(e) $11 450 1% p.a. 6 years
(f) $7 252 8% per month 3 months
(g) $18 200 5% per month 6 months
(h) $32 000 10% per month 7 months
(i) $4 200 12% p.a. compounded monthly 8 months
(j) $5 300 16% p.a. compounded half-yearly 2 years
A B C D E
1 Principal $6000
2 Interest rate (% p.a.) 14
3 Term (years) 5
4
5 Interest rate (% per period) Number of periods Final amount Total interest
6 Simple interest 14 5 $10 200.00 $4 200.00
7 Compound interest
8 compounded yearly 14 5 $11 552.49 $5 552.49
9 compounded half-yearly 7 10 $11 802.91 $5 802.91
10 compounded quarterly 3.5 20 $11 938.73 $5 938.73
11 compounded monthly 1.1667 60 $12 033.66 $6 033.66
12 compounded daily 0.0383 1826.25 $12 080.90 $6 080.90
ACCOUNT FEES AND CHARGES
Banks and credit unions impose fees and charges on their savings accounts, for situations such as:
excessive withdrawals made in a month
accounts with low balances (e.g. less than $500)
ATM withdrawals made at another bank’s ATM
dishonoured cheques: ‘bad cheques’ deposited or withdrawn when there are insufficient
funds in the account
overdrawn accounts: accounts where more money has been withdrawn than there were
funds in the account.
Example 11
OziBank’s CashCard savings account has the following associated fees and charges:
There is also a Government Debits Tax (GDT) on cheque withdrawals, at the following rates:
First 8 withdrawals per month
(not including withdrawals at another bank’s ATM, direct debit or transfers to another bank account: see below)*
Free
Each subsequent withdrawal
– ATM/EFTPOS/cheque withdrawals $0.50
– Phone/Internet banking (for paying bills and transfers) $0.20
– Withdrawal at bank $2.00
* Withdrawal at another bank’s ATM $1.80
* Direct debit Free
Monthly account-keeping fee (for balances below $500) $5.00
Overdrawn account $20.00
Cheque/direct-debit dishonour fee $25.00
Card replacement $5.00
New chequebook $10.00
* Transfers to another bank account (made at bank) $5.00
Yearly dormancy fee (if no transactions made in a year) $10.00
Debit amount GDT
Less than $1.00 nil
$1 to $99.99 $0.30
$100 to $499.99 $0.70
$500 to $4999.99 $1.50
$5000 to $9999.99 $3.00
Manuel has $1420.50 in his CashCard account.
(a) Does he need to pay the monthly account-keeping fee?
(b) During the month, he makes 10 withdrawals from his account, the last two being EFTPOS and a cash withdrawal at the bank. Calculate the charges incurred. (c) Manuel also writes a cheque for $235.50. What amount of GDT must he pay? (d) His deposits in the month total $616.20 and his withdrawals total $502.55. If Manuel
also buys a new chequebook, calculate his final balance after all charges have been applied.
Solution
(a) No, because his account balance is above $500. (b) EFTPOS charge = $0.50, Bank withdrawal = $2.00
Total charges = $0.50 + $2.00 = $2.50 (c) For a $235.50 cheque, GDT = $0.70. (d) Old balance= $1420.50
Total deposits= $616.20 Total withdrawals= $502.55
Total charges= $2.50 + $0.70 + $10.00 = $13.20 Final balance= $1420.50 + $616.20 − $502.55 − $13.20
= $1520.95
Questions 1–8 refer to OziBank’s CashCard savings account on page 382 (Example 11).
1. Jeremy has already made 8 withdrawals from his CashCard account this month. What
will it cost him now to withdraw some money from an ATM?
2. (a) After 8 withdrawals have been made from a CashCard account, which method of
withdrawing money incurs the lowest charge? Why do you think?
(b) Which method of withdrawing money incurs the highest charge? Why do you think?
3. Jess has $287.50 in her account and has lost her card.
(a) What is the cost of acquiring a new card?
(b) Does she have to pay the monthly account-keeping fee? Give a reason for your answer.
(c) During the month, she makes 11 withdrawals from her account, all at her bank’s ATM. How much will she be charged for this?
(d) She then writes a cheque for $82.40. Calculate the charge and the GDT for this transaction.
(e) If Jess’s deposits for the month total $612.40 and her withdrawals (including the cheque) total $541.22, calculate her final balance after all fees have been applied.
4. OziBank imposes a fee if no transactions are made on the CashCard account during the
year.
(a) What is this fee called and how much is it?
(b) Why do you think a bank would impose such a fee?
5. Claire wrote a cheque for $340 when she had only $289.26 in her account.
(a) What type of fee will she be charged? (b) How much is this?
6. Samir had $8061 in his account and made 9 withdrawals, the last one being the payment
of his electricity bill by Internet banking. He then went to his bank branch to transfer $2400 to an account at another bank, and then made a withdrawal of $120 from another bank’s ATM. All of this happened in the same month.
(a) Calculate all of the charges incurred on the account during the month.
(b) If Samir made no deposits and his first 9 withdrawals totalled $831.90, calculate his final balance after all withdrawals and charges had been deducted.
7. Why do you think Ozibank imposes:
(a) a charge for more than 8 withdrawals made in the month? (b) a monthly account-keeping fee for balances below $500? (c) a cheque/direct-debit dishonour fee?
8. Ozibank published a brochure for its customers listing ways of minimising account
charges. Explain how the following suggestions will reduce account charges. (a) If you shop by EFTPOS, ask the retailer if you can also withdraw extra cash. (b) If you currently withdraw small amounts nearly every day, try withdrawing larger
amounts once or twice a week instead.
(c) Pay by credit or direct debit rather than by ATM, EFTPOS or cheque. (d) Combine all of your separate accounts into one account.
(e) Bank via the telephone or the Internet.
9. Why do you think banks prefer you to make a withdrawal at one of their ATMs rather
than:
(a) inside one of their branches? (b) at another bank’s ATM?
1. Obtain a brochure from one or more of the banks or credit unions in your local area and
compare the fees and charges of the different types of savings accounts available. Examine a monthly statement of your own account (or your family’s) and see how and when these fees and charges are applied.
2. Prepare a report comparing the main fees and charges of two different savings accounts,
either within the same bank or between two banks or credit unions.
Investigation:
Account-keeping fees
M
OREEXAM TIPSRead all of the instructions of the exam carefully. Don’t rush.
Don’t panic. Aim to work steadily. Plan your time well and keep an eye on it.
When you have finished a question, make sure you have actually answered it. Do you need to write the answer in a sentence? Put a circle or box around the answer to highlight it.
Make sure that your answer sounds reasonable, especially if it involves money or measurement. Did you round off correctly and include the correct units?
If your working-out is taking too long, stop and think: Am I on the wrong track? Don’t get bogged down. You may need to retrace your steps, start again or come back later.
Once you have completed the exam, go over it again. Double-check your answers, especially the more difficult ones or those of which you are unsure.
INVESTING IN SHARES
As well as saving at a bank or credit union, an investor may buy stocks in an Australian company such as BHP, Woolworths or Qantas. This means that they own part of the company, with their investment being used with those of other shareholders to run the business. The company’s annual profit is divided between all shareholders, and each share of the profit is called a dividend. Dividends are paid once or twice per year.
The price of a share changes continually during each weekday, influenced by demand and supply, the Australian economy and market confidence in the company. A shareholder may profit by buying shares at a low price and selling them at a higher price. The original price of a share, usually 50c, $1 or $2, is called its face value while the current price is called its
market value or market price.
Investing in shares is riskier than investing in a bank, but the dividends earned can be far greater. There are two types of shares: ordinary shares and preference shares. Preference shareholders receive their dividends first, at a fixed predetermined rate (like bank interest), while the dividend from an ordinary share is variable. The dividend yield (or annual yield) is the dividend expressed as a percentage of the share’s market value.
Agents who buy and sell shares are called stockbrokers. A stockbroker’s commission, usually around 2%, is called brokerage. Most investors own shares in more than one company. A collection of shares from different companies is called a portfolio.
Note: Stocks and shares mean the same thing. You can buy and sell stock in a company, and
one unit of stock is called a share.
Example 12
Joanne owns 1000 $2 ordinary shares and 700 $1 preference shares in Coles Myer. The current prices of the ordinary and preference shares are $7.87 and $5.40 respectively. (a) What is the market value of Joanne’s shares?
(b) If the dividend on the ordinary shares is 28c per share and the dividend on the preference shares is 6% of face value, calculate Joanne’s total dividends.
(c) Calculate the dividend yield of Joanne’s ordinary shares correct to 1 decimal place.
Solution
(a) Market value= 1000 × $7.87 + 700 × $5.40
= $11 650
(b) Dividends on ordinary shares= 1000 × $0.28
= $280
Dividends on preference shares= 6% × 700 × $1
= $42 Total dividends= $280 + $42
= $322
Dividend yield= dividend per share × 100% market price of share
---(c) Dividend yield= × 100%
= × 100%
= 3.5578 …%
≈ 3.6%
Example 13
Anh bought 1000 Telstra shares at $5.80 each, with a dividend yield of 5.6%. Brokerage costs were 2.5% of the purchase price, while stamp duty (state tax) was 15c per $100 or part thereof.
(a) Calculate the total cost of purchasing the shares.
(b) One year later, Anh sold all of his shares at $6.50 each. Calculate his total earnings for the year, after costs.
Solution
(a) Cost of shares= 1000 × $5.80
= $5800 Brokerage= 2.5% × $5800
= $145
Stamp duty= $0.15 × 58 15c per $100
= $8.70
Total cost= $5800 + $145 + $8.70
= $5953.70 (b) Dividend= 5.6% × $5800
= $324.80 Selling price= 1000 × $6.50
= $6500
Earnings= selling price + dividend − total costs
= $6500 + $324.80 − $5953.70
= $871.10
Information about share prices is supplied by the Australian Stock Exchange (ASX) and can be found in the Finance section of daily newspapers or on the Internet. Over 1200 Australian companies are listed on the ASX, in industries such as mining and oil (e.g. Rio Tinto), banking (St George), media (Prime TV), transport (TNT), food (Coca-Cola Amatil) and retail (Harvey Norman).
1. Visit the Australian Stock Exchange’s website www.asx.com.au and play the share market game. It asks you to choose how many shares you wish to purchase in six companies, then calculates the value of your investment after a given number of years, using real prices.
2. Read the Finance section of a newspaper and interpret the information about shares
presented in a table.
3. Write the names of eight companies that are listed on the Australian Stock Exchange and
list their market prices and dividend yields. dividend per share market price of share
---$0.28 $7.87
1. Adrian wants to purchase 2500 shares in C & W Optus. The market price of the shares
is $3.54.
(a) Calculate the total cost of the shares.
(b) The stockbroker charges a basic order fee of $20 plus a commission of 2% of the cost of the shares. Calculate the total brokerage.
(c) Calculate the stamp duty if it is 60c per $100 or part thereof.
(d) A dividend of 47c was paid when the market price of the share was $2.62. Calculate the dividend yield correct to 2 decimal places.
2. Terry bought 4000 $2 preference shares for $8920. They have a 12% dividend of face
value. Calculate:
(a) the market price of 1 share (b) the total dividend earned
(c) the dividend yield correct to 2 decimal places
3. A stockbroker charges the following rates of brokerage:
2.5% of share value up to $5000 2% of the next $10 000
1.5% of the next $35 000 1% of the remainder
Colin buys 800 shares in David Jones at $1.49 each. Calculate: (a) the cost of the shares, including the brokerage
(b) the stamp duty if it is 30c per $100 or part thereof
(c) his total dividend and dividend yield to 2 decimal places, given that the dividend is 11c per share when the market price is $1.20
4. Eliza bought 200 $2 shares in Fairfax and paid $780 for them. Calculate:
(a) the market price of 1 share
(b) the dividend per share (to the nearest cent) if the dividend yield is 6.2%
5. Zeli bought 40 000 shares in Western Metals at $0.58 each. Her stockbroker charged
2.5% brokerage for the first $15 000 of shares and 0.75% thereafter. Stamp duty was 30c per $100 or part thereof.
(a) Calculate Zeli’s total cost of purchasing the shares.
(b) If Zeli collects a dividend yield of 4.8% and then she sells all her shares at $0.74 each, calculate her total earnings after costs.
6. Vicky owns 4200 $1 ordinary shares and 3000 $2 preference shares in the Ten Network.
(a) Calculate the total face value of her shares.
(b) The shares cost $2.70 per ordinary share and $4.33 per preference share, and the additional costs were:
Broker’s service fee: $5.50
Brokerage: 2.5% of share value up to $5000 2% of the next $10 000
1.5% of the next $35 000 1% of the remainder.
Calculate the total cost of buying the shares.
(c) If the company pays a dividend of 28c per ordinary share and 7% of face value per preference share, determine Vicki’s total dividend.
(d) Calculate the dividend yield of an ordinary share correct to 2 decimal places.
7. Village Roadshow shares have a face value of $2, a market value of $3.40 and pay a
dividend of 12.5% of face value.
(a) Adrian owns 300 shares. What is their total market value? (b) What is the total dividend earned?
(c) Calculate the dividend yield correct to 1 decimal place.
8. Karl manages the following share portfolio.
(a) Calculate the total value of the shares. (b) Calculate the total dividends earned.
9. George owns 2500 AGL shares. The dividend per share is 42c and the market price is
$8.37.
(a) What dividend will George receive on his shares? (b) Calculate the dividend yield correct to 1 decimal place.
(c) How many extra shares could George purchase if he reinvested his dividend?
10. Caltex 50c shares have a market price of $2.60. If the dividend is 35% of face value,
calculate the dividend yield correct to 2 decimal places.
11. Paula bought 5500 50c ordinary shares and 2500 $2 preference shares in Qantas.
(a) Calculate the total face value of her shares.
(b) If the company pays a dividend of 14c per ordinary share and 7.3% per preference share, determine Paula’s total dividend.
(c) If the market prices of the ordinary and preference shares are $2.80 and $4.93 respectively, calculate correct to 1 decimal place:
(i) the value of Paula’s share portfolio
(ii) the dividend yield on Paula’s ordinary shares
12. Sandy bought 3500 shares in Fosters Brewing at $6.49 with a dividend yield of 7%.
Brokerage was 2.5% of the first $5000, 2% of the next $10 000, 1.5% of the next $35 000 and 1% thereafter. Stamp duty was 30c per $100 or part thereof.
(a) Calculate the total cost of purchasing the shares.
(b) If Sandy sells her shares 1 year later at $7.14 each, find her total profit after costs.
Like any specialised field, the share market has its own jargon or specific terminology. You may have seen or heard the following words used in the financial section of a newspaper or on TV/radio news programs. Find out what they mean:
Bear market bid blue-chip stocks
Bull market capital gains tax CHESS
dividend reinvestment float par value
P/E ratio prospectus speculation
No. of shares Company Market value Dividend yield
1000 Pacific Mining $1.87 3.3%
600 Air New Zealand $2.49 6%
800 TAB $3.13 5.1%
1700 Cadbury $8.62 5.2%
SHARE TABLES AND GRAPHS
Daily information about share prices can be found in the Finance section of a newspaper or on the Internet, listed in a table like this.
Key
52 week high/low: the maximum and minimum prices of the share in the last 52-week period (in dollars)
Last sale: the market price of the share (in dollars)
Move: the change in cents of the market price compared to yesterday’s price
Buy: the highest buying price offered during the day
Sell: the lowest selling price offered during the day
Div. cents: the dividend per share in cents
Div. yield %: the dividend yield
52 week
Company
Last
sale Move Buy Sell
Div. cents
Div. yield % High Low
12.29 8.53 AGL 8.70 −9 8.68 8.70 45.00 5.17
4.00 2.35 Angus and Coote 3.80 3.21 3.80 20.00 5.26
1.75 1.25 Just Jeans 1.28 +3 1.24 1.28 10.00 7.81
5.40 2.38 Qantas 4.93 +19 4.95 4.76 19.00 3.85
5.93 4.15 Seven Network 4.45 +6 4.45 4.50 20.50 4.61
1.91 0.95 Sydney Gas 1.468 +1.8 1.47 1.48 4.00 2.72
3.58 2.63 TAB 2.66 −1 2.65 2.66 9.00 3.38
12.11 9.15 Westpac 9.548 −0.2 9.60 9.51 45.00 4.71
Just for the record
A
LLO
RDINARIESI
NDEXOne statistic that summarises the state of the Australian stock market is a figure called the
All Ordinaries Index, sometimes abbreviated All Ords. Like share prices, this is a value
that changes continually each weekday. It is calculated from the prices of 500 different shares representing 90% of share transactions. It is called an ‘all ordinaries’ index because it is based on the prices of ordinary shares.
The All Ordinaries Index was created in January 1980, beginning with a base value of 500. In 1999, its value was around the 2000–3000 mark. Every day, the index rises or falls by a number of points, reflecting the movements of share prices, and the final closing value is reported in newspapers, on the nightly TV news and on the Internet.
1. Find the value of today’s All Ordinaries Index.
2. Other countries have different indices for measuring the state of their stock markets.
Example 14
From the share table on page 389:
(a) What is the market price of Qantas shares? (b) What was their price yesterday?
(c) What was the lowest price of AGL shares over the past 52 weeks? (d) Which share paid a dividend of 20.5 cents?
(e) What was the lowest selling price of Just Jeans shares during the day? (f) What was the dividend yield on TAB shares?
(g) If the TAB dividend was paid today, what would it be (to the nearest 0.1c)?
Solution
(a) $4.93(b) Qantas rose 19c today, so its share price yesterday was $4.93 − $0.19 = $4.74. (c) $8.53
(d) Seven Network (e) $1.28
(f) 3.38%
(g) 3.38% × $2.66 = $0.089 908 ≈ 9.0c
Example 15
This graph shows the performance market price of Orica shares over 6 months.
(a) What was its highest price during this period? (b) How many times did the price reach $8.40? (c) Describe the performance of the share over the
period.
(d) Predict what will happen to the share price after 15 October.
Solution
(a) Approximately $9.50. (b) 6 times.
(c) The price shot up rapidly around May, then gradually declined while still fluctuating daily, then started gradually increasing around 15 October.
(d) It looks like the price may gradually increase again.
1. Use a graphics calculator, spreadsheet or graphing software to input and graph the
market price of a particular share over a period. Use published share data to create a table of the company’s share price over the period first.
2. Graph the changes in the All Ordinaries Index over the same period and compare its
performance with that of your share.
9.60 9.40 9.20 9.00 8.80 8.60 8.40 8.20 8.00 7.80
SHARE PRICE $
Orica
15 Apr 15 Oct
Source: Bloomberg, Sydney Morning Herald, 16 October 1999.
Questions 1–8 refer to the share table on page 389.
1. For Angus and Coote shares:
(a) What was the dividend yield? (b) What is the market price?
(c) There were no sales yesterday. How is this shown in the table? (d) What was the lowest price in the past 52 weeks?
(e) What was the lowest buying price in the past 24 hours? (f) What was the dividend?
2. (a) Which share showed the smallest change in price from yesterday?
(b) What was this change?
3. (a) Which share showed the greatest change in price from yesterday?
(b) What was this change?
4. (a) Which share has the highest market price?
(b) Which share has the lowest market price?
5. Which share(s) paid a dividend of:
(a) 45c? (b) 10c? (c) 9c?
6. Which share had the lowest market price in the past 52 weeks?
7. (a) What is Sydney Gas’s current share price?
(b) What was its price yesterday?
(c) What would be the dividend per share if it was paid today?
8. (a) Which share has a market price of $9.548?
(b) Which share had a high of $12.11 in the past 52 weeks? (c) Which had the largest drop in price from yesterday? (d) Which had a dividend yield of 7.81%?
(e) Which had a highest selling price of $8.70 during the day?
9. For the graph of Orica share prices on page 390 (Example 15), find:
(a) the market price on 15 April (b) the lowest price over the period
(c) the number of months covered by the period (d) the number of times the price reached $9.00 (e) the price on 15 October
(f) an estimate for the price on 15 November
10. This graph shows the performance of National
Mutual shares over 6 months.
(a) What was the highest price over this period? (b) What was the lowest price?
(c) How many times did the price reach $2.60? (d) Estimate the price at 22 July.
(e) Describe the performance of the share in the first 3 months.
(f) Describe the performance of the share in the last 3 months.
Exercise 10-06:
Share tables and graphs
2.80 2.70 2.60 2.50 2.40 2.30 2.20 2.10
SHARE PRICE $
22 Apr 22 Oct National
Source: Bloomberg, Sydney Morning Herald, 23 October 1999.
(g) What do you think may happen to the share price after 22 October?
(h) Would after 22 October be a good time to sell? Give reasons for your answer.
11. This graph shows the performance of Flight
Centre shares over 6 months.
(a) How is the performance of Flight Centre shares different from the performances of Orica and National Mutual shares (pages 390 and 391)?
(b) Describe the performance of Flight Centre shares over the period. (c) Estimate the share price in:
(i) April (ii) July
(iii) October
(d) When did the price of the share reach the $8 mark?
(e) When did the share price rise the quickest?
(f) Would October be a good time to buy or sell Flight Centre shares? Why?
1. In groups of three to five, pretend that you are investing in the stock market. Given a
spending account of $10 000, create a share portfolio and purchase shares in up to eight different companies. For every week over a term of 10 weeks, keep track of the prices of your shares. You can buy and sell your shares at any time. Also take note of the All Ordinaries Index. At the end of the term, sell all of your shares at the buyer’s price.
2. Calculate your total dividends and the total profit or loss on your investment.
3. Construct graphs showing the performances of one of your shares and the All Ordinaries
Index. Compare the two graphs.
INFLATION AND APPRECIATION
Inflation
The prices of goods and services rise almost every year, and this is usually accompanied by increases in workers’ wages and salaries. This is called inflation, and the percentage by which prices increase each year is called the annual inflation rate. Recently, the inflation rate in Australia has remained fairly low at 0 to 5%, but it has been as high as 13% in the past.
Calculating price rises after inflation is an application of increasing an amount by a percentage; but if the inflation rate remains constant, then we can use the compound interest ‘final amount’ formula.
12.00 11.00 10.00 9.00 8.00 7.00 6.00 5.00
SHARE PRICE $
Flight Centre
Apr 99 Oct 99
Source: Bloomberg, Sydney Morning Herald, 12 October 1999.
Modelling activity:
Investing in the stock market
A = P(1 + r)n where A is the final price,
P is the initial price,
Example 16
A particular model of car costs $28 500 today. Calculate the price of a similar model of car in 5 years’ time (to the nearest $100) if the inflation rate remains constant at 3% p.a.
Solution
P = $28 500, r = 0.03, n = 5
Price in 5 years, A= $28 500(1 + 0.03)5
= $28 500(1.03)5
= $33 039.3111 …
≈ $33 000
Example 17
The current price of a magazine is $5.50. Calculate its price 10 years ago (to the nearest 10c) if the inflation rate during this time was 1.4% p.a.
Solution
A = $5.50, r = 0.014, n = 10
Current price, $5.50 = P(1 + 0.014)10
= P(1.014)10
Price 10 years ago, P =
= $4.7861 …
≈ $4.80
Appreciation
Most items decrease in value over time as they become old and out-of-date. This is called
depreciation. However, some items increase in value
over time, such as jewellery, gold, antiques, prestige cars, art, stamp collections, land and houses. They become more valuable as time passes because they become more rare or scarce. This is called
appreciation. Some people like to invest their money
by buying and selling such items.
Calculating the value of an item after appreciation is another application of percentage increase and the compound interest formula (where r is the annual rate of appreciation).
Example 18
A block of land with a value of $85 000 appreciates at a rate of 6.5% p.a. Calculate its value after 3 years.
Solution
P = $85 000, r = 0.065, n = 3
Value after 3 years, A= $85 000(1 + 0.065)3
= $85 000(1.065)3
= $102 675.718 …
≈ $102 675.71 $5.50 1.014
( )10
---1. A loaf of bread currently costs $2.00. Calculate its price in 5 years if the inflation rate is
4.7% p.a.
2. A 15-day holiday package costs $2300. Calculate its cost in 2 years’ time if the inflation
rate is 6.1% p.a.
3. A textbook today costs $40.00. What was its price 8 years ago if the inflation rate over
this period was 4% p.a.?
4. If gold appreciates at 9.3% p.a. and its current value is $459 per ounce, calculate its value
in 5 years’ time.
5. A collection of Beatles memorabilia appreciates at 4.8% p.a. and is currently valued at
$12 400. What will be its value in 9 years?
6. Name two or three items that appreciate in value over time.
7. A house increased in value this year from $247 000 to $263 055. What was the rate of
appreciation?
8. An accounting executive’s salary increases with the annual inflation rate of 2.1%.
Calculate her salary in 3 years if it is currently $59 020.
9. A pair of jeans costs $45 today. What was its value 10 years ago if the inflation rate was
3.5% p.a.?
10. How much will $50 be worth by today’s standards in 5 years’ time if the inflation rate is
2.4% p.a.? Hint: Final value = $50.
11. Calculate the cost of a $649 refrigerator in 6 years if the inflation rate is 4% p.a.
Just for the record
C
ONSUMERP
RICEI
NDEX(CPI)
While the All Ordinaries Index summarises the prices of Australian shares, the Consumer
Price Index (CPI) summarises the prices of 100 000 Australian goods and services. It is
a value that is calculated quarterly by the Australian Bureau of Statistics, based on the prices of food, clothes, houses, household equipment, transport, health care, recreational and educational items, tobacco and alcohol.
Like the All Ordinaries Index, the CPI means nothing on its own. It is used for comparing prices and the cost of living between two different times, and noting changes in them over the period. The CPI was last set at a base value of 100 in the 1989–90 financial year and during the 1990s it rose to the 120 mark. The annual rate of inflation is calculated from the CPI of consecutive years, using the formula
Inflation rate = × 100%
1. Find the current CPI by visiting the Australian Bureau of Statistics Internet website
www.abs.gov.au.
2. Calculate this year’s inflation rate using this year’s and last year’s CPIs.
new CPI–old CPI old CPI
12. An antique lamp has a current value of $290. What was its value 15 years ago (to the
nearest dollar) if it has appreciated at 6.3% p.a.?
13. Katrina has a pearl necklace worth $1100. What will be its value after 12 years if it
appreciates by 9% annually?
14. A stamp collection appreciates at 3.3% every year. Its present value is $4800.
(a) What was its value 5 years ago? (b) What will be its value in 5 years?
15. A car costs $28 500. What was the value of a similar earlier model 10 years ago if the
inflation rate was 3.4% p.a.?
16. A movie ticket costs $14.50 today. What will be its price in 4 years’ time if the inflation
rate is 1.6% p.a.? Answer to the nearest 10c.
17. What was the price of an apartment 15 years ago if its current value is $234 000 and it
has appreciated at 4% p.a.? Answer to the nearest $1000.
18. An artwork appreciates by 10% each year. Calculate its value in 20 years if its current
value is $18 000.
19. By guessing-and-checking, find how long it will take prices to double if the annual
inflation rate is 4%. Answer to the nearest year.
20. What will $100 buy in today’s terms in 10 years if the inflation rate is 1.5% p.a.?
L
OOKING AFTERYOURSELFWhile studying, don’t forget to keep it all in perspective. Remember to have your own life, outside of school.
Look after your health, physical and mental. Eat and sleep properly. Exercise, play sport and go out occasionally.
Relax and rest regularly. Plan to do nothing occasionally. Talk to your family, visit your friends. Be positive, be sensible.
Have confidence in yourself. Don’t get stressed.
Don’t worry, be happy.
C
hapter review
Savings and investments
1. Simple interest 2. Compound interest 3. Interest tables and graphs 4. Account fees and charges 5. Investing in shares 6. Share tables and graphs
7. Inflation and appreciation
This chapter, Savings and investments, examined the mathematics of saving and investing money. Be sure to understand the calculations and formulas involved in finding simple and compound interest, and the tables and graphs associated with these. Be prepared to apply the compound interest formula to problems involving investment accounts, inflation and appreciation. As there was a lot of new content in this chapter, note these areas in your summary: account charges, purchasing shares in a company, and interpreting share prices presented in a table and graph. There is also considerable financial jargon in this chapter, especially related to the stock market, so a glossary in your study notes would be handy. Make a summary of this topic. Use the chapter outline above as a guide. An incomplete mind map has been started below. Use your own words, symbols, diagrams and boxes. Make connections, look for general principles and include personal observations and reminders. Use the questions in Your say below to think about your understanding of the topic. Gain a ‘whole picture’ view of the topic and identify any weak areas.
Have you satisfied the outcomes listed at the front of this chapter?
What was the most important thing that you learned?
How did you feel about the topic? Did you enjoy it?
What was new?
What are your weaknesses? What will you need to study more?
How will you revise and summarise this topic?
Topic summary
Savings and
investments
Compound interest A = P(1 + r)n
Shares Inflation and
appreciation
Interest tables and graphs Simple interest
I = Prn
1. Calculate the simple interest earned from the following investments.
(a) $7200 at 6.25% p.a. for 3 years (b) $4050 at 3% p.a. for 16 months (c) $10 300 at 0.75% per month for 2 years
2. An investment of $8900 earned $2002.50 in simple interest after 5 years. What was
the annual interest rate?
3. For how long must a principal of $4000 be invested at 6.6% p.a. for it to earn $2376
in simple interest?
4. Calculate the final amounts of the following investments and the compound interest
earned.
(a) $7200 at 6.25% p.a. for 3 years
(b) $4050 at 3% p.a. for 16 months, compounded monthly (c) $10 300 at 0.75% per month for 2 years, compounded monthly
5. Calculate the size of the investment when $1000 is invested at 5% p.a. for 2 years and
the interest is:
(a) compounded annually (b) compounded half-yearly (c) compounded quarterly
6. Describe how the frequency of compounding affects the size of the total interest.
7. What amount of principal must be invested at 5.8% p.a. for it to grow to $15 000 in
8 years if:
(a) simple interest applies? (b) compound interest applies? Answer to the nearest cent.
8. Match the following situations to their graphs below.
(a) simple interest I earned from an investment of $6000 at 3% p.a. over n years (b) simple interest I earned from an investment of $6000 at 15% p.a. over n years (c) the amount of an investment A after $5000 are invested at 2.25% p.a. compound
interest
(d) the amount of an investment A after $5000 are invested at 10.75% p.a. compound interest.
9. OziBank’s Incentive Saver account charges a monthly account-keeping fee if the
balance falls below $800. There is no charge for the first five withdrawals in a month, but any further withdrawals incur a fee of 80c each. Last month, Charlotte made eight withdrawals from her account, leaving her with a balance of $685.81. Calculate the total charges and fees made to her during the month.
Chapter assignment
10. Use a value from the table below to calculate the compound interest earned when $900
are invested at 10% p.a. for 2 years, compounded half-yearly.
11. Maddison bought 4000 shares in CSR at a price of $3.80 with a dividend yield of 6.5%.
Brokerage costs were 1.8% of the purchase price. Stamp duty was 30c per $100 or part thereof.
(a) Calculate the total costs of purchasing the shares.
(b) One year later, Maddison sold her shares for $4.80 each after collecting her dividends. Calculate her total earnings for the year, after costs.
12. QBE Insurance shares have a face value of $2, a market value of $6.41 and pay a
dividend of 14% of face value.
(a) Parker bought 350 shares. How much did they cost him? (b) How much dividend was he paid?
(c) Calculate the dividend yield correct to 2 decimal places.
13. This graph shows the performance of Cable and
Wireless Optus shares over a period.
(a) How long is the period covered by this graph? (b) What was the lowest share price over this
period, and in which month did it occur? (c) Describe the performance of the share over
the period.
(d) How many times did the price reach $3.50? (e) Estimate the value of the share at 22 October. (f) Would after 22 October be a good time to buy
or sell? Give reasons for your answer.
14. A TV set currently costs $549. Assuming an inflation rate of 2% p.a., calculate to the
nearest dollar the price of the TV set:
(a) 10 years from now (b) 10 years ago
15. A $5000 diamond ring appreciates in value at 4.5% p.a. Calculate its value in 25 years.
16. Raymond is keeping his first pay cheque of $519.50 and framing it. If he decides to
cash this cheque in 10 years’ time, what will it be worth in today’s terms if the annual inflation rate over this period is 2.2%. Hint: Let the final value be $519.50.
Compounded values of $1 Interest rate per period
Periods 1% 5% 10%
1 1.010 1.050 1.100
2 1.020 1.103 1.210
3 1.030 1.158 1.331
4 1.041 1.216 1.461
5 1.051 1.276 1.611
SHARE PRICE $
Optus
Cable & Wireless
3.80 3.70 3.60 3.50 3.40 3.30 3.20 3.10
6 Aug 22 Oct
