NZ Level 6 (NZC) Level 1 (NCEA)
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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.

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 $B_n$Bn is the closing balance at the end of $n$n years, find the value of $B_0$B0

c

Write a recursive rule that gives the closing balance, $B_n$Bn, 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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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.

Outcomes

NA6-3

Apply everyday compounding rates

91026

Apply numeric reasoning in solving problems

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