Extra repayments, frequency changes and offsets | Year 12

01 / LEARN

The idea, step by step

Extra repayments change later interest

An extra repayment reduces the loan balance immediately after it is made. That smaller balance earns less interest in later periods. Recalculate the remaining schedule from the new balance rather than merely subtracting the extra cash from total interest.

If comparing repayment frequencies fairly, state both the rate conversion and the annual cash budget. For a fixed effective annual rate e and f periods per year, use $i = {(1 + e)}^{1 / f} - 1$ . Paying half a monthly payment every fortnight increases annual payments because there are 26 fortnights, not 24.

An offset reduces the interest base

In the simplified offset model here, interest is charged on $max (B - O, 0)$ , while the loan balance B remains separate from offset funds O. The offset money is still an asset; it has not automatically repaid principal.

Specify the timing of deposits or withdrawals from the offset account. The recurrence is $B_{k + 1} = B_{k} + i max (B_{k} - O, 0) - R$ . A comparison with a lump-sum repayment must consider both remaining debt and money still held in the offset account, not the debt number alone.

A common trap

Assuming half the monthly payment every fortnight gives the same annual cash outflow.

Instead: There are 26 fortnights, so 26 half-payments equal 13 monthly payments, not 12.

02 / WORKED EXAMPLES

See the thinking

Example 1

Build the model

AUD 10,000 is owed at 0.5% monthly, with AUD 500 repayments. Compare the balance after 12 months with and without an extra AUD 1,000 paid immediately at time 0.

Reduce the initial principal to AUD 9,000 in the extra-payment model.
Apply the same 12 payments and interest rate.
The difference exceeds AUD 1,000 because later interest is saved.

No extra: AUD 4,449.00; extra: AUD 3,387.32; balance difference AUD 1,061.68.

Example 2

Use the model to make a decision

A loan balance is AUD 30,000, an offset holds AUD 5,000, and the monthly rate is 0.5%. Find the month’s interest.

Interest base is $m a x (30000 - 5000, 0) = 25000$ .
Interest is $25000 \times 0.005 = 125$ .

AUD 125.00

Check your understanding

Find the fortnightly rate equivalent to an effective annual rate of 6%.

Show answer

0.2244%

There are 26 model periods per year. $i = {1.06}^{1 / 26} - 1$ .

03 / WORKSHEET

Your turn

6 questions · 18 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

A monthly repayment is AUD 800. Compare the annual cash paid with AUD 400 paid every fortnight.
3 marks
Find the fortnightly rate equivalent to an effective annual rate of 6%.
3 marks
A balance is AUD 20,000 with an offset of AUD 3,000. Interest is 0.4% monthly and the month-end repayment is AUD 600. Find the new loan balance.
3 marks
A debt of AUD 1,500 has an offset of AUD 2,000. Under a model with no negative interest and an AUD 200 month-end repayment, find the new debt.
3 marks
A no-interest loan of AUD 6,000 is repaid at AUD 300 monthly. How many months are saved by instead paying AUD 400 monthly?
3 marks
Explain why an offset balance of AUD 4,000 is not the same accounting entry as a permanent AUD 4,000 principal repayment.
3 marks

Read the worked solutions

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

A monthly repayment is AUD 800. Compare the annual cash paid with AUD 400 paid every fortnight.
3 marks
Monthly total is $12 \times 800 = 9600$ .
Fortnightly total is $26 \times 400 = 10400$ .
Monthly: AUD 9,600.00; fortnightly: AUD 10,400.00; extra annual outflow AUD 800.00.
Find the fortnightly rate equivalent to an effective annual rate of 6%.
3 marks
There are 26 model periods per year.
$i = {1.06}^{1 / 26} - 1$ .
0.2244%
A balance is AUD 20,000 with an offset of AUD 3,000. Interest is 0.4% monthly and the month-end repayment is AUD 600. Find the new loan balance.
3 marks
Interest is $(20000 - 3000) \times 0.004 = 68$ .
Loan balance is $20000 + 68 - 600 = 19468$ .
The AUD 3,000 remains in the offset; it is not subtracted from the debt again.
AUD 19,468.00
A debt of AUD 1,500 has an offset of AUD 2,000. Under a model with no negative interest and an AUD 200 month-end repayment, find the new debt.
3 marks
The interest base is $m a x (1500 - 2000, 0) = 0$ .
New debt is $1500 - 200 = 1300$ .
AUD 1,300.00
A no-interest loan of AUD 6,000 is repaid at AUD 300 monthly. How many months are saved by instead paying AUD 400 monthly?
3 marks
At AUD 300, $6000 / 300 = 20$ months.
At AUD 400, $6000 / 400 = 15$ months.
Difference is 5 months.
5 months
Explain why an offset balance of AUD 4,000 is not the same accounting entry as a permanent AUD 4,000 principal repayment.
3 marks
Both may initially reduce the interest base by AUD 4,000.
Compare net positions and access to cash, not only the loan’s displayed balance.
The offset leaves both the loan debt and an accessible savings asset; a principal repayment reduces the debt and uses the cash.

Checking saved progress…

Continue learning

Comparison rates and choosing between loan models

Next lesson

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 ↗

Back to Financial mathematics