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Which is better: Simple or compound interest?

In document NELSON SENIOR MATHS ESSENTIALS 12 (Page 131-135)

simple or compound

interesl?

INVESTIGATION

simple interest? Is compound interest always better than

It's a common misconception that compound interest always gives a better return than simple interest. In this investigation, you are going to make some calculations to help you choose the investment with the better return.

What you have to do

• Copy the following table or print a copy from NelsonNet.

• Use the technology of your choice to complete the following 3 summaries. To make it easier, make the principal $1000 in every calculation.

• Complete the class discussion questions after you have finished the calculations.

Which is better: Simple or compound interest?

Part A

The interest rates and the term are the same. Simple interest investment

Term: 4 years Interest rate: 5% p.a. Term: 6 years Interest rate: 3% p.a. Term: 20 years Interest rate: 7.5% p.a.

PartB

Annually compound interest investment

Term: 4 years Interest rate: 5% p.a. Term: 6 years Interest rate: 3% p.a.

Term: 20 years Interest rate: 7.5% p.a.

Summary

Simple interest =

Compound interest =

Which investment is better?

Simple interest =

Compound interest =

Which investment is better? Simple interest =

Compound interest =

Which investment is better?

The term is the same but the compound rate is higher than the simple interest rate. Simple interest investment

Term: 4 years Interest rate: 5% p.a. Term: 6 years

Interest rate: 3.75% p.a. Term: 20 years Interest rate: 7.5% p.a.

Annually compounded interest investment

Term: 4 years Interest rate: 5.1 % p.a. Term: 6 years Interest rate: 4% p.a.

Term: 20 years Interest rate: 8.1 % p.a.

Summary

Simple interest =

Compound interest =

Which investment is better? Simple interest =

Compound interest = Which investment is better?

Simple interest =

Compound interest =

Which investment is better?

PartC

The terms are the same but the simple rate is higher than the compound interest rate.

Simple interest investment

Term: 4 years Interest rate: 5% p.a.

Term: 6 years Interest rate: 3% p.a. Term: 20 years Interest rate: 12% p.a.

Term: 3 years Interest rate: 12% p.a. Class discussion questions

Annually compounded interest investment

Term: 4 years

Interest rate: 4.8% p.a.

Term: 6 years

Interest rate: 2.75% p.a.

Term: 20 years Interest rate: 7.5% p.a.

Term: 3 years Interest rate: 7.5% p.a.

Summary Simple interest = Compound interest = Which investment is better? Simple interest =

Compound interest = Which investment is better? Simple interest =

Compound interest= Which investment is better? Simple interest =

Compound interest = Which investment is better?

• When the interest rates and the term are the same, does simple or compound interest give the better return?

• When the compound rate is higher than the simple interest rate, and the terms are the same, which type of investment produces the better return?

• When the simple rate is bigger than the compound rate, and the terms are the same, will one or the other type of interest always give the better return?

IIJI INTEREST RATES AND SAVINGS

Compound interest is amazing. You might be surprised how quickly it helps regular savings accumulate. Banks and building societies have savings and investment accounts that pay compound interest. In addition, some accounts offer bonus interest to encourage you to deposit money without making any withdrawals.

Most bank websites and the MoneySmart website contain savings calculators. To complete the following example and exercises, you will need access to an online calculator, the spreadsheet on NelsonNet or a programmable calculator with a TVM menu.

1

1i"l

I

Monlhly saving� calculator

Monthly savings calculator

0 Example 6

Jessica has $2400 in an account that pays 3.5% p.a. interest. She needs to have $80 000 in 5 years from now. How much will she need to save per month to reach her goal?

Solution

There are a variety of technologies we can use to solve this problem. This solution uses the Savings Term calculator on the

Commonwealth Bank website. It is located in the 'tools' section.

Enter 3.5 for the Interest Rate, 2400 for Jessica's Current Balance, 80 000 for the target Deposit Amount and 5 years for the Savings Term.

Enter:

Interest Rate

Current Balance of Savings Target Deposit Amount Savings Term Calculate

I

Result:

Amount to Save Per Month

I 3.s %p.a. $12400 $180 000

15

years

I

Months Clear

I

$11174.92

I

Jessica will need to save $1174.92 every month to reach her target.

EXERCISE 5.04

Interest rates and savings

You will need access to online calculators to complete this exercise.

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Use the Commonwealth Bank's 'Monthly savings calculator' to determine how much each person needs to save every month to reach their target.

Home Interest Current Target

buyer rate balance amount

a Madelaine 3.3% $1500 $9000

b Isaac 2% $1750 $8000

C Liam 5.1% Nil $25 000

d Ellen 3.75% $5000 $45 000

e Aidan 9% Nil

Savings Monthly savings term required 4 years 3 years 5 years 6 years 5 years 6months

2 Amanda has $4000 in her account and she needs $20 000 in 5 years time.

a How much will she need to invest each month to reach her goal when interest rates are

3% p.a.?

b How much will she need to contribute per month if interest rates are 8% p.a.?

c If interest rates increase to 10% p.a., how much will Amanda need to contribute monthly? d Write a sentence to describe the relationship between interest rates and the amount you

need to save per month to reach a target.

Use the Commonwealth Bank's 'Savings term calculator' to answer questions 3 to 5. 3 Chelsea has $1300 in a savings account that pays 4.2% p.a. interest. She deposits

$300 per month into the account. How long will it take before there is $6000 in her account? 4 Thomas has a special savings account that pays 5% p.a. interest. At the moment he only has

$100 in the account but he is going to deposit $500 into the account each month. When will there be more than $18 000 in the account?

5 Chloe is going to start to save the deposit for her first home. She is going to deposit $600 per month into an account. How much quicker will she be able to save $50 000 when interest rates are 7% p.a. compared to 3% p.a.?

Use the Commonwealth Bank's 'Target deposit amount calculator' to answer questions 6 and 7. 6 Jonathan is saving $320 each month in an account that pays 5% p.a. The current balance of the

account is $4200. How much will be in the account in one and a half years time?

7 The balance in Maddison's acc_ount is $2150. The account pays 4.7% p.a. interest and each month Maddison deposits $420 into the account. How much will be in her account in 4 years time? 8 Group discussion and investigation question.

Imagine that you need to save $30 000 for the deposit on your first house. a What savings interest rates are banks offering at the moment?

b How could you increase your income to make it possible to save more? c How much can you afford to save each month?

d How long will it take you to save the deposit?

e Imagine that you have a partner who can save the same amount per month that you can. How long will it take the two of you to save the deposit?

Suppose that interest rates fall when you are saving. What effect will this have on the time it will take to save the deposit?

In document NELSON SENIOR MATHS ESSENTIALS 12 (Page 131-135)