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.

a

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 | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

b

If $B_n$`B``n` is the closing balance at the end of $n$`n` years, find the value of $B_0$`B`0

c

Write a recursive rule that gives the closing balance, $B_n$`B``n`, at the end of year $n$`n`.

d

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.

e

At the end of which year will the loan have been repaid?

Easy

Approx 13 minutes

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