### 0 Example 4

Bevan invested $2000 at 5% p.a. interest compounded annually. Calculate the value of his investment at the end of three years.

### Solution

We need to calculate the interest for each year separately and add it to the principal before we calculate the following year's interest.

**Interest at the end of ** **Balance at the end of **
**the year ** **the year **

**End of the first year ** **J ****= Prn**

### =

$2000**X**0.05

**X**1

### =

$100**End of the second year ** **J ****= Prn**

**= **$2100 **X **0.05 **X **1
**= **$105

**End of the third year ** **J **

### =

*Prn*

### =

$2205 X 0.05 X 1### =

$110.25 $2000 + $100**=**$2100 $2100 + $105

### =

$2205 ' $2205 + $110.25### =

$2315.25At the end of three years, Bevan's investment is worth $2315.25. (He earns $2315.25 - $2000

### =

$315.25 in interest)### EXERCISE 5.02

**Compound interest **

**•§irn,,dl **

Yuri invested $8000 at 6% p.a. interest compounded annually for 3 years. Copy and
complete this table to calculate the value of her investment at the end of three years.

**End of the first year **

**End of the second year **

**End of the third year **

**Interest at the end of the year **
*l=Prn *

### =

$8000**X**0.06

**X**1 =$ _ _

*l=Prn*=$ __ xo._x1 =$_

*l=Prn*=$ __ xo. __ x 1 =$ __

**Balance at the end of the year **

$8000+$_ =$ __ $ _ _ +$_ =$ __ $ __ +$ __ =$ _ _

2 Jayden invested $12 000 for 3 years at 4% p.a. compounding yearly. a How much interest did he earn in the first year?

b How much was in his account at the end of the first year?

c How much was in his account at the end of the second year? d Calculate the value of his investment at the end of three years.

e How much interest will Jayden earn during his 3-year investment?

3 Nazneen invested $4000 at 3.2% p.a. for 2 years compounding annually. a Calculate the total value of her investment at the end of the 2 years. b How much interest will she earn during the two years?

c How much more interest will Nazneen earn than she would have earned if the interest had been simple interest?

4 Suresh has saved $14 000 from his after school job that he plans to spend on a car. He is going to invest the money for 3 months until he has his red-Ps. Suresh's investment is going to pay 0.7% per month, monthly compounding interest.

a Copy and complete the table.

**Interest at the end of the month **

**I[ **

**Balance at the end of the month**

**,End .of the first month**

*l=Prn*$14 000+$ __

= $14 000 X 0.007 X 1 =$_ =$ __

**End of the second �onth ** *l=Prn * _{$ __ +$ __ }

=$_ xo. Xl =$ __

=$_

**End of the third month ** *l=Prn * _{$ __ +$ __ }

=$ __ xo._x1 =$

=$ __

b How much interest will Suresh make during the 3-month investment?

5 Kirrilly invested some money in monthly compounding interest. The table shows her interest and balance calculations.

**Interest at the end of the month Balance at the end of the month **

**End of the first month **
**End of the second month **

*l=Prn *
= $9600 X 0.008 X 1
= $76.80
*I= Pm *
= $9676.80 X 0.008 X 1
= $77.41

a How much.money did Kirrilly invest?

b What was the monthly rate of compound interest?

$9600 + $76.80 = $9676.80

$9676.80 + $77.41 = $9754.21

c Convert the monthly rate to an annual rate of compound interest. d How much interest did Kirrilly's investment earn?

6 Last night, Isabella received an unexpected phone call from an investment advisor she doesn't know telling her about a good investment opportunity that is virtually risk-free. The offer is likely to be fully subscribed quickly, so she has to invest straight away if she wants to be part of it and the advisor will phone her again in the morning to start getting the investment

organised. Investment units are $10 000 each and the interest rate is 15% p.a. annually compounding for 3 years.

a Calculate the amount of interest the advisor claims each unit will receive in the next 3 years. b Why should Isabella be very cautious about investing in this opportunity?

7 Rachel decided that calculating compound interest was too time-consuming so she created a spreadsheet to do the calculations automatically. Her spreadsheet allows her to alter the principal and interest rate. The spreadsheet is available on NelsonNet.

**A ** **B **

**1 Compound interest **
**2 Only enter doto in cells shaded blue. **

**4 **
**5 **
**6 **

**Principal ** **$1.000.00 **

**C **

**Annual rate of interest as a **
**percentage **
**D **
**12% **
**7 **
**8 **
**9 **
**10 **
**11 **
**12 **
**13 **
**14 **
**15 **

**Account balance at the beginning **

**of the year ** **Interest earned during the year ** **Account bolonce ot the end of theyeu **

**Year 1 **
**Year 2 **
**Year3 **
**Yeor4 **
**Year 5 **
**Year6 **
**Year 7 **
**Yeor8 **
**$1.000.00 **
**$1.120.00 **
**$120_.00 **

a What formulas could Rachel have used for cells BS, D8 and B9?

b Rachel used the formula =B8*$D$4. Why did she use the two $ signs? c Use 'fill down' to complete the spreadsheet calculations for 8 years.

**$1.120.00 **

d Use the spreadsheet to determine the amount of interest a $4500 investment will earn in 8 years at 4.8% p.a. annually compounding interest.

8 This graph shows the total value on a $1 compound investment at 3% p.a., 6% p.a. and 10% p.a.

10%

a Describe how the shape of a compound interest graph is different to the shape of a simple interest graph.

### ---

**�--6%**

**3%**

b Approximately how long does it take for a $1 investment to double its value at 10% p.a. compound interest?

I 2 3 4 5 6 7 8 9 10 11

9 Nick and Adam invested the same amount of money at 9% p.a., but Nick's investment was 9% p.a. compounded annually while Adam's was 9% p.a. simple. The graphs show the value of their investments after 5 years.

a How much was Nick and Adam's original inve�tment?

Years � 600 '.;' 550

### i

500 ] 450 � 400*X*

*y*o�����.-..

**Compound**

**interest**

SCAMwotch

### INVESTIGATION

_{Is it a scam? }

The Internet and technology have changed the way we do things and made life easier for us. But technology has also made life easier for criminals to use scams and financial fraud to rob people of their hard-earned money.

Visit the SCAMwatch website.

**2 ** Open the tab **How scams work. **List 4 different reasons why people fall for scams.
**3 ** Prepare a list of answers you could give to possible scammers when they are trying to

convince you to do something you don't want to do.

**4 ** Open the tab **Have you been scammed? **at the top of the page. Describe what you should
do if you have sent money to someone you think is a scammer.