7.03 Loans
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.
Dylan takes out a loan to purchase a property. He makes equal monthly loan repayments of \$4600 over 27 years to pay it off. Calculate the total amount paid back on the loan.
Gwen takes out a loan to purchase a surround sound system. She makes 11 equal loan repayments. The total loan amount paid back is \$6600.
Calculate the amount 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.
Jimmy takes out a loan of \$700 to purchase a computer. The loan earns interest at 6\% p.a. compounded annually. Repayments of \$140 are made annually.
Calculate the amount Jimmy still owes after his first repayment.
Calculate the amount Jimmy still owes after his second repayment.
Kathleen takes out a loan of \$88\,000 to renovate her home. The loan earns interest at 8\% p.a. compounded monthly. Repayments of \$11\,264 are made annually.
Calculate the amount Kathleen will still owe after the first repayment.
Calculate the amount Kathleen will still owe after the second repayment.
Han received a 9-year \$43\,000 loan at 10\% p.a. monthly reducible interest. He makes monthly instalments of \$209.
Find the amount owing after:
1 month
2 months
3 months
Is the amount owing increasing or decreasing?
Will this loan eventually be paid off if the instalments remain the same? Explain your answer.
Joanne takes out a loan of \$54\,000 to purchase a plot of land. The loan earns interest at 2\% p.a. compounded annually. Repayments of \$864 are made annually.
How much interest is added to Joanne's loan in the first year?
Calculate the amount Joanne still owes after the first repayment.
Should Joanne continue to make annual payments of \$864? Explain your answer.
Suggest a better annual payment amount for Joanne's loan.
Luke takes out a loan of \$73\,200 to start a business. The loan earns interest at 8\% p.a. compounded annually. State whether the loan will be paid off in 3 years if the following amounts are repaid monthly:
\$1627
\$2034
\$2562
Valentina is deciding between two \$109\,000 home loans. She has the capacity to pay \$3400 per month.
Option 1: 3.2\% p.a. over 3 years with fixed monthly repayments of \$3179.
Option 2: 2.6\% p.a. over 3 years with minimum monthly repayments of \$3151 that enables paying more than the minimum monthly repayment
What is the total repayment she will have to make with Option 1?
What is the maximum total repayment she will have to make with Option 2?
Which loan will cost less?
Ivan takes out a car loan for \$24\,000. He is charged 8.1\% per annum interest, compounded monthly. Ivan makes repayments of \$450 at the end of each month.
Complete the following table which tracks the loan over the first three months:
| Month | Opening Balance | Interest | Repayment | Closing Balance |
|---|---|---|---|---|
| 1 | 24\,000 | 162 | 450 | 23\,712 |
| 2 | ||||
| 3 |
A car loan of \$6000 earns interest at 8\% p.a. compounded annually. Repayments of \$720 are made annually.
Complete the following table which tracks the loan over the first three years:
| \text{Time period} \\ (n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$6000 | |||
| 2 | \$460.80 | \$720 | ||
| 3 | \$5500.80 | \$720 |
A loan of \$54\,000 earns interest at 5.4\% p.a. compounded monthly. Repayments of \$1500 are made monthly.
Complete the following table which tracks the loan amount over the first three months:
| \text{Time period} \\ (n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$243.00 | \$1500 | \$52\,743 | |
| 2 | \$237.34 | |||
| 3 | \$51\,480.34 | \$231.66 | \$1500 |
Dave took out a loan of \$6500 to start his business on January 1. Interest on the loan is charged at 10\% p.a. from the time the loan is taken out. He made yearly repayments of \$2500 on December 31 each year.
Complete the repayment table:
| Year | Balance owing at beginning of year | Interest charged in this period | Balance owing at end of year | Balance owing after repayment |
|---|---|---|---|---|
| 1 | ||||
| 2 | ||||
| 3 |
Find the amount of interest charged between his first and second repayment.
Monthly repayments of \$3990 are made on a loan of \$158\,800 borrowed at a rate of 12\% p.a. compounded monthly.
Consider the following table of home loan repayments:
| \text{Month }(n) | \text{Principal }(P) | \text{Interest }(I) | P + I | P + I - R |
|---|---|---|---|---|
| 1 | \$158\,800 | \$1588.00 | \$160\,388.00 | \$156\,398.00 |
| 2 | \$156\,398.00 | \$1563.98 | \$157\,961.98 | \$153\,971.98 |
| 3 |
What is the principal at the beginning of the third month?
Calculate the interest charged for the third month.
How much money is owed at the beginning of the fourth month?
The following table shows the principal and interest over the first 4 months of a loan:
| \text{Month} | P | I | P +I | P + I - R |
|---|---|---|---|---|
| 1 | \$20\,000 | \$50.00 | \$20\,050.00 | \$19\,150.00 |
| 2 | \$19\,150.00 | \$47.88 | \$19\,197.88 | \$18\,297.88 |
| 3 | \$18\,297.88 | \$45.74 | \$18\,343.62 | \$17\,443.62 |
| 4 | \$17\,443.62 | \$43.61 | \$17\,487.23 | \$16\,587.23 |
Find the value of each repayment, R.
What is the annual interest rate charged on the loan to the nearest percent?
Calculate the value of the principal at the start of month 6.
Kate takes out a personal loan for \$40\,000. The interest on the loan is charged quarterly and Kate makes repayments of \$900 at the end of each quarter.
Calculations for the first quarter are shown in the following table:
| Quarter | Opening Balance | Interest | Repayment | Closing Balance |
|---|---|---|---|---|
| 1 | 40\,000 | 400 | 900 | 39\,500 |
| 2 | ||||
| 3 |
Calculate the quarterly interest rate Kate is charged for this loan as a percentage.
State the annual interest rate of this loan as a percentage.
Calculate the values for Quarters 2 and 3 in the table.
How much of the loan has Kate repaid in the first three quarters of the year?
Maximilian takes out a mortgage to purchase an investment property. A number of his payments and balances are shown in the following table:
| Month | Opening Balance | Interest | Repayment | Closing Balance |
|---|---|---|---|---|
| 1 | x | 3500 | 417\,970 | |
| 2 | 417\,970 | 1462.90 | 3500 | |
| 3 | y |
Calculate the monthly interest rate charged on this loan as a percentage. Round your answer to two decimal places.
Calculate the annual interest rate charged on this loan as a percentage. Round your answer to two decimal places.
Calculate the value of x, the initial amount borrowed for this mortgage.
Calculate the value of y in the table.
A study abroad loan of \$8500 earns interest which is compounded monthly. Repayments of \$2550 are made half yearly. The following table documents the repayment of the loan:
| \text{Time period} \\ (n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$8500 | \$416.25 | \$2550 | \$6366.25 |
| 2 | \$6366.25 | \$311.76 | \$2550 | \$4128 |
| 3 | \$4128 | \$202.15 | \$2550 | \$1780.15 |
| 4 | \$1780.15 | \$87.17 | \$1867.33 | \$0 |
Calculate the total loan amount paid.
A small loan of \$4500 to pay for a holiday earns interest at 4\% p.a. compounded annually. Repayments of \$2000 are made annually.
Complete the following table which tracks the loan amount over three years:
| \text{Time} \\ \text{period } (n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$4500 | \$2000 | ||
| 2 | \$107.20 | |||
| 3 | \$787.20 | \$0 |
Why is the repayment in the third year smaller than the other repayments?
Calculate the total loan amount paid.
You take out a personal loan of \$10\,000 at 11\% reducible p.a. The term of the loan is 3 years, and yearly repayments of \$2600 are made. The balance owing is paid at the end of 3 years.
Complete the loan repayment table:
| Time period | Balance owing at beginning of period | Balance owing plus interest during period | Repayment | Balance owing at end of period |
|---|---|---|---|---|
| 1 | 10\,000 | 2600 | ||
| 2 | 2600 | |||
| 3 |
Find the total amount of interest charged on the loan.
Find the total repayment over 3 years.
A study abroad loan of \$13\,600 earns interest at 2.4\% p.a. compounded monthly. Repayments of \$4080 are made either half-yearly or yearly.
Complete the following table which tracks the repayment of the loan with half-yearly payments:
| \text{Time} \\ \text{period }(n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$13\,600 | \$164.02 | \$4080 | |
| 2 | \$9684.02 | \$116.79 | ||
| 3 | \$5720.81 | \$68.99 | \$4080 | |
| 4 | \$0 |
What is the total loan amount paid if making half yearly repayments?
Complete the following table that tracks the repayment of the loan with yearly payments:
| \text{Time} \\ \text{period }(n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$13\,600 | \$330.01 | \$8160 | |
| 2 | \$5770.01 | \$140.01 |
What is the total loan amount paid if making yearly repayments?
What is the better payment option in order to reduce the total amount paid?
\$3700 is invested for three years at a rate of 7\% p.a., compounded annually.
Complete the table below to determine the final value of the investment:
| Balance at beginning of year | Interest earned | |
|---|---|---|
| First year | \$3700 | \$259 |
| Second year | \$3959 | \$277.13 |
| Third year | ||
| Fourth year | - |
Calculate the total interest earned over the three years.
Mr and Mrs Lyne have a \$520\,000 mortgage for their home. They are charged 5.16\% interest per annum, compounded monthly and make monthly repayments of \$3750.
Complete the table below, using the rounded answer to calculate the amounts for the following month:
| \text{Month } | \text{Opening Balance } (\$) | \text{Interest }(\$) | \text{Repayment }(\$) | \text{Closing Balance }(\$) |
|---|---|---|---|---|
| 1 | 520\,000 | 2236 | 3750 | 518\,486 |
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 |
If they made fortnightly repayments of \$1\,875 instead of monthly repayments, what would be the result on the balance of their loan after 10 years?
A \$2000 loan is to be repaid at a reducible rate of 8\% p.a. There are two possible methods of repayment: repaying \$750 every 6 months or repaying \$375 every 3 months, and the interest is compounded at the same interval as payment.
Complete the repayment table, showing repayments made every 6 months:
| Time period | Balance owing at beginning of period | Balance owing plus interest during period | Repayment | Balance owing at end of period |
|---|---|---|---|---|
| 1 | 2000 | 2080 | 750 | |
| 2 | 750 |
Complete the repayment table, showing repayments made every 3 months:
| Time period | Balance owing at beginning of period | Balance owing plus interest during period | Repayment | Balance owing at end of period |
|---|---|---|---|---|
| 1 | 2000 | 2040 | 375 | 1665 |
| 2 | 1665 | 1698.30 | 375 | |
| 3 | 375 | |||
| 4 | 375 |
Calculate the difference in the balances owing after 1 year.
A credit card charges annual interest of 18.24\%.
Calculate the monthly interest rate on this credit card, correct to two decimal places.
Roald owes \$3200 on his credit card and will pay it all off before using this card again. The table displays his payments:
| Month | Interest | Repayment | Amount Owing |
|---|---|---|---|
| 3200 | |||
| 1 | 48.67 | 75 | X |
| 2 | 48.27 | 75 | 3146.93 |
| 3 | Y | 75 | 3119.79 |
| \ldots | \ldots | \ldots | \ldots |
| \ldots | \ldots | \ldots | \ldots |
| 66 | 4.76 | 75 | 242.66 |
| 67 | 3.69 | 75 | 171.35 |
| 68 | 2.61 | 75 | 98.96 |
| 69 | 1.51 | 75 | 25.47 |
| 70 | Z | W | 0 |
Calculate the value of X.
Calculate the value of Y
Calculate the value of Z.
Calculate the value of W.
Calculate the total interest paid.
Xanthe takes out a car loan. The last few months of her repayments are shown in the following table:
| 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 |
| 72 |
Calculate the monthly interest rate charged on this loan, rounding your answer to one decimal place.
Calculate the values for the final row of the table, rounding your answers correct to two decimal places.
How many years did it take for Xanthe to pay off the loan?
Calculate her total repayments.
If her original loan was for \$15\,000, calculate the total interest paid on the loan.
Mr. and Mrs. Dave have a mortgage. The final months of their repayments are shown in the following table:
| 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 |
| 151 |
Calculate the monthly interest rate charged on this loan. Round your answer to two decimal places.
Calculate the values for the final row of the table, rounding your answers to two decimal places.
How many years did it take for them to pay off the loan? Round your answer to two decimal places.
Calculate the total repayments.
If they paid \$302\,097.60 in interest, how much did they initially borrow?
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 5 \\ \text{years} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} |
|---|---|---|---|---|---|
| 10\% | 21.25 | 13.22 | 10.75 | 9.65 | 9.09 |
| 11\% | 21.74 | 13.78 | 11.37 | 10.32 | 9.80 |
| 12\% | 22.24 | 14.35 | 12.00 | 11.01 | 10.53 |
| 13\% | 22.75 | 14.93 | 12.65 | 11.72 | 11.28 |
| 14\% | 23.27 | 15.53 | 13.32 | 12.44 | 12.04 |
| 15\% | 23.79 | 16.13 | 14.00 | 13.17 | 12.81 |
Han received a 5-year \$151\,000 loan at 10\% p.a. monthly reducible interest. If the interest rate was increased to 15\% p.a., find the increase in the amount of each monthly instalment needed to be paid.
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 5 \\ \text{years} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} |
|---|---|---|---|---|---|
| 6\% | 19.33 | 11.10 | 8.44 | 7.16 | 6.44 |
| 7\% | 19.80 | 11.61 | 8.99 | 7.75 | 7.07 |
| 8\% | 20.28 | 12.13 | 9.56 | 8.36 | 7.72 |
| 9\% | 20.76 | 12.67 | 10.14 | 9.00 | 8.39 |
| 10\% | 21.25 | 13.22 | 10.75 | 9.65 | 9.09 |
| 11\% | 21.74 | 13.78 | 11.37 | 10.32 | 9.80 |
Maria received a 5-year \$209\,000 loan at 10\% p.a. monthly reducible interest. If the interest rate fell to 6\% p.a., find the decrease in the amount of each monthly instalment needed to be paid.
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} |
|---|---|---|---|---|---|
| 4\% | 10.12 | 7.40 | 6.06 | 5.28 | 4.77 |
| 5\% | 10.61 | 7.91 | 6.60 | 5.85 | 5.37 |
| 6\% | 11.10 | 8.44 | 7.16 | 6.44 | 6.00 |
| 7\% | 11.61 | 8.99 | 7.75 | 7.07 | 6.65 |
| 8\% | 12.13 | 9.56 | 8.36 | 7.72 | 7.34 |
| 9\% | 12.67 | 10.14 | 9.00 | 8.39 | 8.05 |
Neil received a 10-year \$130\,000 loan at 6\% p.a. monthly reducible interest. If the interest rate was increased to 7\% p.a., find the increase in the total repayments needed to clear the debt.
ANZ offers the choice of two types of loans:
Option 1: 5.2\% p.a. flat rate interest over 25 years.
Option 2: 8.2\% p.a. reducible interest over 15 years.
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} | 35 \\ \text{years} |
|---|---|---|---|---|---|
| 4.2\% | 9.06 | 7.67 | 6.83 | 6.28 | 5.88 |
| 5.2\% | 9.89 | 8.5 | 7.67 | 7.11 | 6.71 |
| 6.2\% | 10.72 | 9.33 | 8.5 | 7.94 | 7.55 |
| 7.2\% | 11.56 | 10.17 | 9.33 | 8.78 | 8.38 |
| 8.2\% | 12.39 | 11 | 10.17 | 9.61 | 9.21 |
| 9.2\% | 13.22 | 11.83 | 11 | 10.44 | 10.05 |
Calculate the total repayments to be made with Option 1 on a \$170\,000 loan.
Calculate the total repayments to be made with Option 2 on a \$170\,000 loan.
Which loan will cost less in total?
Eileen is deciding between two 20-year loans to finance the purchase of a new \$5000 salon.
Option 1: 6\% p.a. reducible interest along with a one-off \$535 loan application fee.
Option 2: 8\% p.a. reducible interest along with a monthly account fee of \$41.
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} | 35 \\ \text{years} |
|---|---|---|---|---|---|
| 4\% | 7.40 | 6.06 | 5.28 | 4.77 | 4.43 |
| 5\% | 7.91 | 6.60 | 5.85 | 5.37 | 5.05 |
| 6\% | 8.44 | 7.16 | 6.44 | 6.00 | 5.70 |
| 7\% | 8.99 | 7.75 | 7.07 | 6.65 | 6.39 |
| 8\% | 9.56 | 8.36 | 7.72 | 7.34 | 7.10 |
| 9\% | 10.14 | 9.00 | 8.39 | 8.05 | 7.84 |
Which loan should she choose? Explain your answer.