 8.02 Simple interest

Worksheet
Simple interest and final value
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 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. 4 \$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.

5

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.

6

Calculate the flat rate interest generated on a loan of \$4290 at a rate of 3\% p.a. for 23 months. 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.

8

Skye takes out a loan of \$800 to pay for an online course. Flat rate interest is charged at 10\% p.a. If she repays the loan in 9 months, how much interest does she pay in total? 9 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. Round your answer to two decimal places if necessary.

10

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.

c

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

d

Interest rate, period and principal
11

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

12

\$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.

13

\$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.

14

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.

15

\$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.

16

\$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.

17

\$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.

18

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.

19

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.