7.03 Interest and loans
Calculate the simple interest on the following:
An investment of \$8840 at 6\% p.a. for 2 years.
A 2-year loan of \$3000 at 17\%. p.a.
A loan of \$8000 at 8\% p.a. for 6 years.
An investment of \$2540 at 9\% p.a. for 2 years.
An investment of \$7000 at 7.2\% for 9 years.
For a simple interest rate of 10\% p.a., calculate the number of years needed for an interest of \$1149.60 to be earned on an investment of \$2874.
Find the annual interest rate as a percentage to one decimal place for the following scenarios:
The simple interest on an investment of \$2650 over 3 years is \$787.05.
The simple interest on a loan of \$2830 over 10 years is \$2603.60.
The simple interest on a loan of \$6600 over 33 months is \$1252.35.
The simple interest on an investment of \$3600 over 2 years is \$504.00.
The simple interest on a loan of \$7550 over 9 years is \$6523.20.
Find the total amount to be paid on a 4-year, \$90\,000 loan at 12\% p.a. flat interest.
The graph shows the amount of simple interest charged each year by a particular bank, on some 9-year loan.
Find the total amount of simple interest charged on a loan of \$4000.
Calculate the simple interest rate per annum charged by the bank on these 9-year loans. Give your answer as a percentage.
Homer borrowed \$7600 from a bank at a simple interest rate of 4.5\% for one year.
How much interest will Homer need to pay after 1 year?
Calculate the total amount Homer will have to repay the bank at the end of 1 year.
\$906 is invested at 5\% p.a simple interest. Dave wants to know the number of years it will take the investment to grow to \$1132.50.
Calculate the interest that will be earned on the investment.
Calculate the number of years it will take the investment to grow to \$1132.50.
If \$4948 is invested at 8\% p.a. simple interest for 7 years, find the simple interest rate that would earn the same amount of interest in only 5 years. Give your answer as a percentage rounded to two decimal places.
For a simple interest rate of 6\% p.a., calculate the number of years needed for an interest of \$1174.20 to be earned on the investment \$1957. Give your answer as a whole number of years.
\$552 is invested at 5\% p.a simple interest. Dave wants to know the number of years it will take the investment to grow to \$828.00.
Calculate the interest that will be earned on the investment.
Calculate the number of years it will take the investment to grow to \$828.00
For a simple interest rate of 8\% p.a., calculate the number of months that \$63\,790 needs to be invested to earn \$7654.80 in interest.
Find the number of years taken to earn the interest.
Hence, find the number of months taken to earn the interest. Give your answer to the nearest month.
For how many years does \$7050 need to be invested for it to grow to \$7950, if simple interest is paid at 7\% p.a.? Round your answer correct to two decimal places.
For his investment into government bonds, Buzz was paid simple interest of 9\% p.a. Calculate the size of Buzz's initial investment if he earned \$294.12 interest after 2 years.
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.
Dave and Emily are looking to invest \$11600 and \$18300 respectively for 6 years. The simple interest rate applied is determined by the following table:
| Principal | Rate p.a. |
|---|---|
| \text{Between } \$4800\text{ and } \$14\,800 | 4\% |
| \text{Between } \$14\,800\text{ and } \$24\,800 | 5\% |
| \text{Greater than } \$24\,800 | 6\% |
How much interest will Dave earn on his investment?
How much interest will Emily earn on her investment?
How much will they earn if they invest their principals together?
How much more interest will they earn by combining their principals?
If \$2196 is invested at 2\% p.a. simple interest for 8 years, what simple interest rate would earn the same amount of interest in only 5 years? Give your answer as a percentage rounded to two decimal places.
Katrina takes out a loan to purchase a surround sound system. She makes 19 equal loan repayments. The total loan amount paid is \$95\,000. Find the value of each repayment.
Lisa takes out a loan to purchase a small boat. She pays it back in equal monthly repayments over 6 years. The total loan amount paid back is \$55\,800. Calculate the amount of each repayment.
Iain takes out a loan to purchase a jetski. He makes 15 equal loan repayments of \$5239. Calculate the total amount paid back on the loan.
Tara takes out a car loan of \$6000 at a simple interest rate of 8\% p.a. She plans to repay the loan over 2 years through regular monthly repayments.
Calculate the total interest that Tara will accrue over the duration of the repayment.
Hence, calculate the value of each repayment of the loan.
A borrower received a loan of \$5500 which was to be repaid in monthly installments of \$269 over 3 years.
Calculate the total repayments.
Calculate the total interest to be paid.
Calculate the flat rate of interest per annum as a percentage to two decimal places.
Sally made loan repayments totalling to \$8960 on a loan of \$8000 over 6 years.
Calculate the total simple interest charged on the loan.
Calculate the annual simple interest rate as a percentage value.
Kathrine took out a loan of \$5600 which was to be repaid in monthly instalments of \$261 over 2 years. Calculate the following, rounding your answers to two decimal places where necessary:
The total repayments.
The total interest to be paid.
The interest as a percentage of the loan.
The effective annual interest rate.
Susana takes out a car loan. The last few months of Susana's repayments are shown below:
| Month | Opening Balance | Interest | Repayment | Closing Balance |
|---|---|---|---|---|
| 69 | 868.48 | 4.34 | 250 | 622.82 |
| 70 | 622.82 | 3.11 | 250 | 375.93 |
| 71 | 375.93 | 1.88 | 250 | 127.81 |
Calculate the monthly interest rate charged on this loan to one decimal place.
Complete the next row of the table for month 72, rounding your answers to two decimal places.
How many years did it take for her to pay off the loan?
Calculate her total repayments.
If her loan was for \$15\,000, calculate the total interest paid on the loan.
Mr and Mrs Maximilian have a mortgage. The final months of their repayments are shown below:
| Month | Opening Balance | Interest | Repayment | Closing Balance |
|---|---|---|---|---|
| 146 | 26\,452.84 | 198.40 | 5000 | 21\,651.24 |
| 147 | 21\,651.24 | 162.38 | 5000 | 16\,813.62 |
| 148 | 16\,813.62 | 126.10 | 5000 | 11\,939.72 |
| 149 | 11\,939.72 | 89.55 | 5000 | 7029.27 |
| 150 | 7029.27 | 52.72 | 5000 | 2081.99 |
Calculate the monthly interest rate charged on this loan. Write your answer as a percentage to two decimal places.
Complete the next row of the table for month 151, rounding your answers to two decimal places.
How long, in years and months, did it take for them to pay off the loan?
Calculate the total repayments.
If they paid \$302\,097.60 in interest, how much did they initially borrow?