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Middle Years

4.09 Simple interest

Worksheet
Simple interest
1

If \$16\,716 of simple interest was earned in 7 years, find how much interest was earned:

a

Each year

b

Each month

2

Ned borrowed \$3600 from a bank at a simple interest rate of 2.5\% p.a.

a

Calculate the interest on the loan in one year.

b

Calculate the interest on the loan after three years.

c

Calculate the total amount Ned will have to repay the bank at the end of 3 years.

3

Buzz takes out 6-year \$50\,000 loan at 8\% p.a. simple interest.

a

Calculate the total interest he will have to pay on the loan.

b

Calculate the total amount he will have to pay back.

4

Calculate the total simple interest to be paid on a 3-year \$8000 loan at 13\% p.a.

5

Calculate the total amount to be paid back on a 5-year loan of \$110\,000 at 5\% p.a. simple interest.

6

Sally pays for her purchase of a new carpet, valued at \$9000, by paying a \$3000 deposit and borrowing the balance at 5\% p.a. simple interest to be repaid over 3 years.

a

Find the total interest she will have to pay.

b

Calculate the total amount she will pay for the carpet.

Different rates and time periods
7

Calculate the simple interest earned on the following investments. Assume that a year has 52 weeks or 365 days.

a

\$2540 at 9\% p.a. for 2 years

b

\$2010 at 6\% p.a. for 13 months

c

\$5320 at 6\% p.a. for 95 weeks

d

\$5440 at 6\% p.a. for 566 days

e

\$7000 at 1.8\% per quarter for 9 years

f

\$1050 at a semiannual rate of 1.1\% for 9 years

8

Calculate the simple interest charged on the following loans. Assume that a year has 52 weeks or 365 days.

a

\$8000 at 8\% p.a. for 6 years

b

\$3860 at 9\% p.a. for 13 months

c

\$5010 at 5\% p.a. for 666 days

d

\$5240 at 4\% p.a. for 73 weeks

9

Calculate the final value of these investments:

a

\$6170 at 5\% p.a. for 6 years.

b

\$9060 at 4\% p.a. for 44 months.

c

\$4230 at 8\% p.a. for 32 weeks.

d

\$4620 at 6\% p.a. for 146 days.

10

Bianca takes out a loan of \$800 to pay for an online course. Simple interest is calculated at 9\% per year, charged monthly. If she repays the loan in 9 months, how much interest does she pay in total?

11

Dave and Emily are looking to invest \$11\,600 and \$18\,300 respectively for 6 years. The table shows the simple interest rates for different principals:

a

Calculate the interest Dave will earn on his investment.

b

Calculate the interest Emily will earn on her investment.

PrincipalRate p.a.
\text{Between \$4800 and \$14\,800}4\%
\text{Between \$14\,800 and \$24\,800}5\%
\text{Greater than \$24\,800}6\%
c

How much will they earn if they combine their principals and invest together?

d

Should they invest separately or together? Explain your answer.

12

Tara takes out a car loan of \$6000 at a simple interest of 8\% p.a. She plans to repay the loan over 2 years through regular monthly repayments.

a

Calculate the total interest that Tara will incur over the duration of the repayment.

b

Calculate the value of each repayment of the loan.

13

\$402 is invested at 4\% p.a. simple interest for 9 years. After this time the principal plus interest is reinvested at 6\% p.a. simple interest for 8 more years.

a

Calculate the value of the investment after 9 years.

b

Calculate the final value of the investment.

c

Calculate the total amount of interest earned.

14

Luke's investment of \$3000 earned simple interest of 4\% p.a. for the first 8 years, and 2\% p.a. for the next 5 years.

Calculate the total amount of interest earned.

Finding rate, principal or time
15

For each of the following investments find the annual simple interest rate, R, as a percentage rounded to one decimal place.

a

\$3600 invested over 2 years earns \$504.00

b

\$4800 invested over 20 months earns \$760.00

c

\$1600 invested over 3 quarters earns \$103.20

16

For each of the following loans find the annual simple interest rate, R, as a percentage rounded to one decimal place.

a

The simple interest on a loan of \$7550 over 9 years is \$6523.20.

b

The simple interest on a loan of \$5800 over 6 quarters is \$321.90.

c

The simple interest on a loan of \$5500 over 24 months is \$385.00.

17

\$1957 is invested at a simple interest rate of 6\% p.a. Calculate the number of years needed for interest of \$1174.20 to be earned on the investment.

18

\$2379 is invested at a simple interest rate of 2\% p.a. Calculate the number of quarters needed for interest of \$23.79 to be earned on the investment.

19

For his investment into government bonds, Scott was paid simple interest of 9\% p.a. Calculate the size of Scott's initial investment \$P, if he earned \$294.12 interest after 2 years.

20

\$63\,790 is invested at a simple interest rate of 8\% p.a. Calculate the number of months needed for interest of \$7654.80 to be earned on the investment. Round your answer to the nearest month.

21

Lisa made loan repayments totalling to \$4320 on a loan of \$4000 over 4 years.

a

Calculate the total simple interest charged on the loan.

b

Calculate the annual simple interest rate.

22

\$552 is invested at a simple interest rate of 5\% p.a.

a

Calculate the interest that will be earned on the investment in one year.

b

Calculate the number of years it will take the investment to grow to \$828.

23

\$7050 is invested at a simple interest rate of 7\% p.a. Calculate the number of years needed for it to grow to \$7950. Round your answer to two decimal places.

24

If \$2196 is invested at 2\% p.a. simple interest for 8 years, what simple interest rate R, would earn the same amount of interest in only 5 years?

Express R as a percentage, correct to two decimal places.

25

The graph shows the amount of simple interest charged each year by a particular bank, on a 3-year loan:

a

Find the total amount of simple interest charged on a loan of \$5000.

b

Calculate the simple interest rate per annum charged by the bank on 3-year loans.

1000
2000
3000
4000
5000
P
50
100
150
200
250
300
I
26

The given graph shows an amount of \$4000 deposited into a savings account for 10 years earning simple interest.

a

How much interest has been earned in total over the 10 year period?

b

Find the interest rate as a percentage, correct to two decimal places.

1
2
3
4
5
6
7
8
9
10
T
3250
3500
3750
4000
4250
4500
4750
A
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