 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.

c

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

d

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. 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.