Tara takes out a loan to purchase a property. The following image depicts the change of the loan over time:
How often is interest being added to the balance of the loan?
How often is Tara making a repayment on the loan?
Tracy takes out a loan to purchase a TV. The following image depicts the change of the loan over time:
How much did Tracy borrow?
How often is interest being added to the balance of the loan?
How often is Tracy making a repayment on the loan?
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} |
|---|---|---|---|---|---|
| 3\% | 9.66 | 6.91 | 5.55 | 4.74 | 4.22 |
| 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\% | 12.17 | 9.56 | 8.36 | 7.72 | 7.38 |
Calculate the monthly instalments required to pay off a 25-year loan of \$1000 at 4\% p.a. monthly reducible interest.
Calculate the monthly instalments required to pay off a 15-year loan of \$125\,000 at 3\% p.a. monthly reducible interest.
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.
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.
A person 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.
Valentina borrowed \$5900 from the bank which was to be paid back in weekly instalments of \$65 over 2 years.
Calculate the following, rounding your answers to two decimal places where necessary:
The total interest to be paid.
The interest as a percentage of the loan.
The effective annual interest rate.
Luke borrowed \$6000 from a finance company. Repayments were in the form of fortnightly instalments of \$132 over 2 years. Calculate the interest on the loan.
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.
Laura takes out a loan of \$86\,000 to renovate her home. The loan earns interest at 8\% p.a. compounded monthly. Repayments of \$11\,008 are made annually.
Calculate the interest on the loan in the first year.
Calculate the balance of the loan after the first repayment.
Calculate the interest on the loan in the second year.
Calculate the balance of the loan after the second repayment.
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.
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.
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 |
Monthly repayments of \$3990 are made on a loan of \$158\,800 borrowed at a rate of 12\% p.a. compounded monthly.
The monthly repayment schedule is shown in the following table:
| \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 |
Calculate the principal at the beginning of the third month.
Calculate the interest charged for the third month.
Calculate the principal at the beginning of the fourth month.
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 intial amount borrowed for this mortgage.
Calculate the value of y in the table.
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 table shows the principal and interest over the first 4 months of a loan:
| \text{Month} | \text{Principal } (P) | \text{Interest } (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 |
How much is each repayment, \text{R}?
Calculate the annual interest rate charged on the loan to the nearest percent.
Calculate the principal at the start of Month 6.
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.
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?
Hermione takes out a loan for \$36\,000. She is charged 7.4\% per annum interest, compounded annually. At the end of each year, she makes a repayment of \$3600.
The following table tracks the loan for the first two years:
| Year | Opening Balance | Interest | Repayment | Closing Balance |
|---|---|---|---|---|
| 1 | 36\,000 | 2664 | 3600 | 35\,064 |
| 2 | 35\,064 | 2494.74 | 3600 | 33\,958.74 |
If B_n is the closing balance at the end of n years, state the value of B_0
Write a recursive rule that gives the closing balance, B_{n+1}, at the end of year n+1.
Use the sequence facility on your calculator to determine how much is owing on the loan after 9 years.
Use the graphing facility on your calculator to graph the balance of the loan, B, against the year n.
At the end of which year will the balance of the loan be \$12\,000?
At the end of which year will the loan have been repaid?
Isabelle takes out a loan for \$170\,000. She is charged 6.7\% per annum interest, compounded annually. At the end of each year, she makes a repayment of \$16\,800.
The following table tracks the loan for the first two years:
| Year | Opening Balance | Interest | Repayment | Closing Balance |
|---|---|---|---|---|
| 1 | 170\,000 | 11\,390 | 16\,800 | 164\,590 |
| 2 | 164\,590 | 11\,027.53 | 16\,800 | 158\,817.53 |
Write a recursive rule that gives the closing balance, B_{n+1}, at the end of year n+1.
Use the sequence facility on your calculator to determine how much is owing on the loan after 10 years.
At the end of which year will the loan have been repaid?
Use the graphing facility on your calculator to graph the balance of the loan, B, against the year n.
Use your graph to estimate how many years it will take to pay off half of the loan.
Use your graph to find the balance of the loan after 5 years.
Vincent takes out a loan for \$68\,000. He is charged 12\% per annum interest, compounded monthly. At the end of each month, he makes a repayment of \$750.
Write a recursive rule that gives the closing balance, B_{n + 1}, at the end of month n + 1.
Use the sequence facility on your calculator to determine how much is owing on the loan after 3 years.
At the end of which year and month will the loan have been repaid?
Ben takes out a loan for \$16\,000. He is charged 7.8\% per annum interest, compounded monthly. At the end of each month, he makes a repayment of \$124.
Use the sequence facility on your calculator to determine how much is owing on the loan after 2 years.
At the end of which year and month will the loan have been repaid?
Kate takes out a loan for \$107\,000. She is charged 4.8\% per annum interest, compounded quarterly. At the end of each quarter, she makes a repayment of \$1700.
Write a recursive rule that gives the closing balance, B_{n + 1}, at the end of quarter n + 1.
Use the sequence facility on your calculator to determine how much is owing on the loan after 5 years.
At the end of which year and quarter will the loan have been repaid?
Use the graphing facility on your calculator to graph the balance of the loan, B, against the quarter n.
Estimate the number of quarters it will take for the balance to be \$80\,000.
Estimate the balance of the loan after 15 years.
Sandy takes out a loan for \$260\,000. She is charged 9.6\% per annum interest, compounded quarterly. At the end of each quarter, she makes a repayment of \$7500.
Write a recursive rule that gives the closing balance, B_{n + 1}, at the end of quarter n+1.
Use the sequence facility on your calculator to determine how much is owing on the loan after 3 years. Give your answer to the nearest dollar.
At the end of which year will the loan have been repaid?
Bart borrows \$61\,000 from a banking institution. He is charged 6.6\% per annum interest, compounded monthly. At the beginning of each month, before interest is charged, he makes a repayment of \$400.
Complete the second row of the following table:
| Month | Opening Balance | Repayment | Interest | Closing Balance |
|---|---|---|---|---|
| 1 | 61\,000 | 400 | 333.30 | 60\,933.30 |
| 2 |
Write a recursive rule that gives the closing balance, B_{n+1}, at the end of month n+1.
Use the sequence facility on your calculator to determine how much is owing on the loan after 4 years.
At the end of which year and month will the loan have been repaid?
Ivan borrows \$270\,000 from a banking institution. He is charged 9.6\% per annum interest, compounded quarterly. At the beginning of each quarter, before interest is charged, he makes a repayment of \$6900.
Complete the second row of the following table:
| Month | Opening Balance | Repayment | Interest | Closing Balance |
|---|---|---|---|---|
| 1 | 270\,000 | 6900 | 6314.40 | 269\,414.40 |
| 2 |
Write a recursive rule that gives the closing balance, B_{n+1}, at the end of quarter n+1.
Use the sequence facility on your calculator to determine how much is owing on the loan after 5 years.
At the end of which year and quarter will the loan have been repaid?
Use the graphing facility on your calculator to graph the balance of the loan, B, against the quarter n.
Estimate the balance of the loan after 20 years.
Describe the rate of change of the balance over the duration of the loan.
Xavier takes out a mortgage to purchase an apartment. At the beginning of each month, after interest is charged, he makes a repayment of \$2900.
The progress of his loan for the first four months is shown in the following table:
| Month | Opening Balance | Interest | Repayment | Closing Balance |
|---|---|---|---|---|
| 1 | X | 2900 | 408\,740 | |
| 2 | 408\,740 | 1634.96 | 2900 | |
| 3 | Y | |||
| 4 |
Calculate the monthly interest rate, r , charged on this loan.
Calculate the value of X in the table.
Calculate the value of Y in the table.
Write a recursive rule that gives the closing balance, A_{n+1}, of the loan after n+1 months and state the initial balance A_0.
Use the sequence facility on your calculator to calculate the value of the final repayment.
Hence calculate the total repayments made.
How much interest does Xavier pay on this loan?
Tara takes out a personal loan to go on a holiday. At the beginning of each quarter, after interest is charged, she makes a repayment of \$350.
The progress of her loan for the first four months is shown in the following table:
| Month | Opening Balance | Interest | Repayment | Closing Balance |
|---|---|---|---|---|
| 1 | X | 10\,831.50 | ||
| 2 | 10\,831.50 | 178.72 | 350 | |
| 3 | Y | |||
| 4 |
Calculate the quarterly interest rate charged on this loan, rounding your answer to two decimal places.
Calculate the value of X in the table.
Calculate the value of Y in the table.
Write a recursive rule that gives the opening balance, A_{n+1}, of the loan at the beginning of n+1 quarters.
Use the sequence facility on your calculator to calculate the value of the final repayment.
Hence calculate the total repayments made.
If Tara had been offered half the rate of interest and everything else remained equal, how would the interest charged on the loan over its lifetime have changed?
Amy buys a car for \$52\,000. She pays a deposit of \$17\,000 from her savings and borrows the remainder through a finance scheme. The interest on the loan is 8.1\% per annum reducible monthly and Amy makes monthly repayments of \$400.
Calculate the amount owed at the end of the first month.
Write a recursive rule, B_{n+1}, that gives the balance of her loan at the end of n+1 months.
Use the sequence facility of your calculator to determine how many months it takes Amy to repay the loan.
Calculate the amount of Amy’s final repayment.
Hence determine the interest paid on the loan.
How much did Amy actually pay for this car?
Michael buys his first house for \$540\,000. He pays a 5\% deposit and receives a first home owners grant of \$15\,000 from the government. He borrows the remainder from a bank. The interest on the loan is 4.8\% per annum reducible monthly and Michael makes monthly repayments of \$3800.
How much is owed at the end of the first month?
Write a recursive rule, B_{n+1}, that gives the balance of the loan at the end of n+1 months.
Use the sequence facility of your calculator to determine how many months it takes for the loan to be repaid.
Calculate the amount of Michael’s final repayment.
How much did Michael actually pay for this house?
If Michael had doubled his monthly repayments and everything else remained the same, how would the length of the loan have changed?