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6.08 Reducing balance loans

Interactive practice questions

Buzz received a 6-year $41000 loan at $8%$8% p.a. monthly reducible interest. He makes monthly instalments of $215.

a

What is the amount owing after 1 month (to the nearest cent)?

b

What is the amount owing after 2 months (to the nearest cent)?

c

What is the amount owing after 3 months (to the nearest cent)?

d

Is the amount owing increasing or decreasing?

Increasing

A

Decreasing

B
e

Will this loan eventually be paid off if the instalments remain the same?

Yes

A

No

B
Easy
4min

Monthly repayments ($R$R)ย of $2920 are made on a loan of $178300 borrowed at a rate of $9%$9% p.a. compounded monthly.

Examine this table of home loan repayments and complete the final row.

Easy
2min

A credit card charges annual interest of $18.24%$18.24%.

Medium
6min

The following table shows the principal and interest over the first 4 months of a loan.

Easy
7min
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Outcomes

4.1.2.1

use a recurrence relation, ๐ด_(n+1)=๐‘Ÿ๐ด_๐‘›โˆ’๐‘… (where ๐‘… = monthly repayment) to model a reducing balance loan and investigate (numerically or graphically) the effect of the interest rate and repayment amount on the time taken to repay the loan

4.1.2.2

with the aid of appropriate technology, solve problems involving reducing balance loans, e.g. determining the monthly repayments required to pay off a housing loan

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