Interest-only loans and sinking funds | Year 12

01 / LEARN

Understand the idea.

Interest-only payments leave the principal owing

An interest-only payment covers the period’s interest but leaves the principal unchanged. With constant principal $P$ and periodic borrowing rate $i$ , every payment is $P i$ . Even after many such payments, the full principal still needs a separate repayment.

A sinking fund is a separate savings account built to meet that later principal payment. Its savings rate $j$ can differ from the borrowing rate. Track the debt and savings separately so their balances and interest charges are not confused.

\begin{aligned} I & = P i \\ S & = R \frac{{(1 + j)}^{n} - 1}{j} \end{aligned}

Combine the cash-flow amounts, not the rates

For a fund starting from zero with equal end-of-period deposits, solve $S = R \frac{{(1 + j)}^{n} - 1}{j}$ . Divide the target $S$ by the savings factor to find $R$ . If an initial fund already exists, subtract its grown value from the target first.

The regular cash budget must cover loan interest plus the fund deposit. Only the interest payment is borrowing interest; the deposit builds a separate asset. Use consistent dates and rates when comparing alternatives, and state that the fund target depends on its assumed return.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Build the model

An interest-only loan is AUD 30,000 at 6% annually. Find its annual interest payment and the principal still owing after 5 interest payments.

Worked solution

1
Calculate the annual interest-only payment.
$I = 30000 \times 0.06 = AUD 1800.00$
Interest is charged on the unchanged AUD 30,000 principal each year.
2
Identify the principal repaid in each payment.
$1800 - 1800 = 0$
The entire payment covers interest, leaving none to reduce the debt.
3
State the debt after five interest payments.
$P_{5} = AUD 30000.00$
Five interest payments keep the loan serviced but do not repay any principal.

Answer

Annual interest AUD 1,800.00; principal still owing AUD 30,000.00.

EXAMPLE 02

Use the model to make a decision

A sinking fund must reach AUD 30,000 in 5 years. At 4% annually, find each equal year-end deposit.

Worked solution

1
Set the fund target at the fifth year end.
$30000 = R \frac{{(1.04)}^{5} - 1}{0.04}$
The five deposits occur at year ends and accumulate at the fund’s 4% savings rate.
2
Solve for each annual deposit.
$\begin{aligned} R & = \frac{30000 \times 0.04}{{(1.04)}^{5} - 1} \\ \approx 5538.813405 \end{aligned}$
Dividing by the ordinary-annuity factor distributes the target across the five deposits.
3
State the deposit to cents.
$R \approx AUD 5538.81$
This is the rounded sinking-fund deposit; loan interest is separate. A cents-only schedule needs a small final top-up, or AUD 5,538.82 equal deposits, to guarantee the target.

Answer

AUD 5,538.81

03 / YOUR TURN

Try it yourself.

Check your understanding

A no-interest sinking fund must reach AUD 18,000 after 36 month-end deposits. Find each deposit.

Show answer & reasoning

AUD 500.00

With zero interest, the 36 equal deposits must total AUD 18,000. Hence $36 R = 18000$ and $R = 500$ , so each deposit is AUD 500.00.

Keep practising

6 worksheet questions · 17 marks

Open worksheet Worked solutions

Read the questions online

Find the monthly interest-only payment on AUD 48,000 at 6% nominal annually, charged monthly.
3 marks
A no-interest sinking fund must reach AUD 18,000 after 36 month-end deposits. Find each deposit.
3 marks
For a loan with annual interest-only cost AUD 1,200 and a sinking-fund deposit AUD 2,600 each year, find the annual cash outflow.
3 marks
A sinking fund has AUD 4,000 now and must reach AUD 15,000 in 4 years at 3%. Find each year-end deposit.
3 marks
A fund accumulates AUD 24,000 from 6 deposits of AUD 3,500. Find the interest earned by the fund.
3 marks
An interest-only loan and sinking fund share a 5-year end date. Explain why interest-only payments alone do not meet the final debt.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find the monthly interest-only payment on AUD 48,000 at 6% nominal annually, charged monthly.
3 marks
Monthly rate is $\frac{0.06}{12} = 0.005$ .
Interest is $48000 \times 0.005 = 240$ .
AUD 240.00
A no-interest sinking fund must reach AUD 18,000 after 36 month-end deposits. Find each deposit.
3 marks
At zero interest, $S = n R$ .
$R = \frac{18000}{36} = 500$ .
AUD 500.00
For a loan with annual interest-only cost AUD 1,200 and a sinking-fund deposit AUD 2,600 each year, find the annual cash outflow.
3 marks
Both payments must be budgeted.
$1200 + 2600 = 3800$ ; only the AUD 1,200 is loan interest.
AUD 3,800.00
A sinking fund has AUD 4,000 now and must reach AUD 15,000 in 4 years at 3%. Find each year-end deposit.
3 marks
Grow the current savings: $4000 {(1.03)}^{4}$ .
The deposits must supply the remaining target.
Divide that remainder by $s_{4} (0.03)$ .
AUD 2,509.30
A fund accumulates AUD 24,000 from 6 deposits of AUD 3,500. Find the interest earned by the fund.
3 marks
Total deposits is $6 \times 3500 = 21000$ .
Fund interest is $24000 - 21000 = 3000$ .
AUD 3,000.00
An interest-only loan and sinking fund share a 5-year end date. Explain why interest-only payments alone do not meet the final debt.
2 marks
Track the principal separately from periodic interest.
Confirm the fund target matches the debt still owing at maturity.
They pay for borrowing during the term but do not reduce the principal; the sinking fund or another source must provide the final principal.

Checking saved progress…

Curriculum reference & lesson scope

SACE Board of South Australia

Stage 2 General Mathematics financial models: investments and annuities, superannuation, income streams and borrowing. Original practice uses supplied hypothetical rates, taxes and fees; statutory or commercial conditions are not inferred.

Official curriculum source ↗

In this lesson

Understand the idea.

Interest-only payments leave the principal owing

Combine the cash-flow amounts, not the rates

See the method in action.

Build the model

Calculate the annual interest-only payment.

Identify the principal repaid in each payment.

State the debt after five interest payments.

Use the model to make a decision

Set the fund target at the fifth year end.

Solve for each annual deposit.

State the deposit to cents.

Try it yourself.

Check your understanding

Keep practising