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Middle Years

9.02 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

Assuming that a year has 365 days and 52 weeks, calculate the simple interest earned on the following investments:

a

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

b

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

c

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

d

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

e

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

f

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

3

Assuming that a year has 365 days and 52 weeks, calculate the simple interest charged on the following loans:

a

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

b

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

c

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

d

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

4

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?

5

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, r, charged by the bank on 3-year loans.

1000
2000
3000
4000
5000
P
50
100
150
200
250
300
I
6

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 \$4\,800 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.

7

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.

Final value
8

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.

9

\$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.

Principal, rates and time
10

The simple interest earned on each investment is given below. Find the annual interest rate r, as a percentage, correct to one decimal place:

a

\$3600 over 2 years is \$504.00.

b

\$1600 over 3 quarters is \$103.20

c

\$4800 over 20 months is \$760.00

d

\$7550 over 9 years is \$6523.20.

e

\$5800 over 6 quarters is \$321.90 .

f

\$5500 over 24 months is \$385.00.

11

Find the principal that earned:

a

\$865 simple interest, at 3\% p.a. over 6 years.

b

\$390 simple interest, at 2.5\% p.a. over 4 years.

c

\$1200 simple interest, at 1\% per month over 2 years.

d

\$3260 simple interest, at 2.5\% per week over 6 months.

12

Sally 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 r, the annual simple interest rate.

13

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

14

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.

15

\$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.

16

\$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.

17

\$2379.00 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.

18

\$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.

19

\$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.

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