Modelling a Loan
Interactive practice questions
Hermione takes out a loan for $\$36000$$36000. She is charged $7.4%$7.4% per annum interest, compounded annually. At the end of each year, she makes a repayment of $\$3600$$3600.
Fill in the missing values in the table. Give all values correct to the nearest cent and use your rounded answers for all subsequent calculations in the table.
| Year | Opening Balance | Interest | Repayment | Closing Balance |
|---|---|---|---|---|
| 1 | $36000$36000 | $2664.00$2664.00 | $3600$3600 | $35064.00$35064.00 |
| 2 | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
| 3 | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
| 4 | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
If $B_n$Bn is the closing balance at the end of $n$n years, find the value of $B_0$B0
Write a recursive rule that gives the closing balance, $B_n$Bn, at the end of year $n$n.
Use the sequence facility on your calculator to determine how much is owing on the loan after $9$9 years.
Give your answer to the nearest cent.
At the end of which year will the loan have been repaid?
Isabelle takes out a loan for $\$170000$$170000. She is charged $6.7%$6.7% per annum interest, compounded annually. At the end of each year, she makes a repayment of $\$16800$$16800.
Vincent takes out a loan for $\$68000$$68000. He is charged $12%$12% per annum interest, compounded monthly. At the end of each month, he makes a repayment of $\$750$$750.
Ben takes out a loan for $\$16000$$16000. He is charged $7.8%$7.8% per annum interest, compounded monthly. At the end of each month, he makes a repayment of $\$124$$124.