Mathematics Advanced • Year 12 • Module 7 • Lesson 15
Extra Repayments, Offset Accounts and Redraw
Practise HSC-style writing on extra-repayment and offset mathematics, plus an extended response on the most efficient cash strategy.
1. Short-answer questions
1.1 A $300,000 home loan at 5.4% p.a. compounded monthly has a minimum repayment of $1,837/month. The borrower pays $2,000/month.
(a) State r per month and Pr ÷ Mnew.
(b) Use nnew = −ln(1 − Pr ÷ Mnew) ÷ ln(1 + r) to find the new term in months and years (1 dp).
(c) State how many years are saved versus the 30-year minimum schedule. 3 marks Band 3
1.2 A $450,000 loan has a $60,000 offset balance. The loan rate is 5% p.a. compounded monthly.
(a) State the effective balance and the monthly interest saving caused by the offset.
(b) State the annual interest saving (12 × monthly saving). 3 marks Band 3-4
1.3 A borrower considers three places to keep $20,000: (i) in an offset account against a 5% p.a. home loan, (ii) in a redraw on the same loan, (iii) in a savings account paying 4% p.a. with interest taxed at 32.5%.
(a) Compute the after-tax benefit of (iii).
(b) State whether (i) and (ii) deliver the same mathematical saving and identify which is more accessible.
(c) Rank the three options from best to worst by after-tax annual return on $20,000. 4 marks Band 4
2. Extended response
2.1 A 30-year-old has a $400,000 home loan at 5% p.a. compounded monthly. The minimum monthly repayment is $2,147. They have just received a $50,000 inheritance. They are considering four options.
Option W: Place the $50,000 in an offset account against the loan.
Option X: Pay the $50,000 as a lump-sum extra repayment on the loan.
Option Y: Invest the $50,000 in a term deposit at 4.5% p.a. with interest taxed at 32.5%.
Option Z: Use the $50,000 to buy shares with an expected (untaxed) return of 6% p.a., but with market risk.
(a) Compute the annual after-tax benefit of each option for the first year, treating the loan-related options as tax-free interest savings at the loan rate.
(b) Rank the four options from highest to lowest first-year benefit and state the dollar gap between #1 and #4.
(c) Explain in 3-4 sentences why W and X have very similar first-year benefits but very different practical profiles, referencing accessibility, reversibility and the long-term compounding effect on the loan. 8 marks Band 5-6
Explicit marking criteria
Part (a) — 4 marks
• 1 mark — correct benefit for Option W (50,000 × 0.05 = $2,500/yr).
• 1 mark — correct benefit for Option X (same $2,500/yr tax-free interest avoided in Year 1).
• 1 mark — correct after-tax benefit for Option Y (50,000 × 0.045 × 0.675 = $1,518.75/yr).
• 1 mark — correct expected (untaxed) benefit for Option Z (50,000 × 0.06 = $3,000/yr).
Part (b) — 2 marks
• 1 mark — correct ranking Z > W ≈ X > Y.
• 1 mark — correct dollar gap Z − Y = $1,481.25/yr.
Part (c) — 2 marks
• 1 mark — identifies that W and X both reduce the interest charged on the loan (W via the offset, X via principal) and both deliver the same numerical year-one saving.
• 1 mark — notes that W keeps the cash accessible (transaction account) whereas X is largely irreversible unless the loan has a redraw facility, and that both options compound over the life of the loan by reducing the principal that future interest is charged on.
Your response:
Stuck on (c)? Reference the lesson's "Offset vs Redraw" table: same mathematical benefit, different accessibility.How did this worksheet feel?
What I'll revisit before next class:
1.1 — $300,000 at 5.4%, Mnew = $2,000 (3 marks)
Sample response. (a) r = 0.054 ÷ 12 = 0.0045. Pr ÷ Mnew = 300,000 × 0.0045 ÷ 2,000 = 1,350 ÷ 2,000 = 0.675. (b) nnew = −ln(0.325) ÷ ln(1.0045) = 1.1239 ÷ 0.004490 ≈ 250.3 months (≈ 20.9 years). (c) Years saved = 30 − 20.9 ≈ 9.1 years.
Marking notes. 1 mark — correct r and ratio. 1 mark — correct n in months and years. 1 mark — correct years saved. Watch for students who forget the negative sign on ln(1 − Pr/M).
1.2 — $450,000 loan with $60,000 offset at 5% (3 marks)
Sample response. r = 0.05 ÷ 12 ≈ 0.004167. (a) Effective balance = 450,000 − 60,000 = $390,000. Monthly saving = 60,000 × 0.004167 = $250.00/month. (b) Annual saving = 250 × 12 = $3,000/yr.
Marking notes. 1 mark — correct effective balance. 1 mark — correct monthly saving. 1 mark — correct annual saving.
1.3 — Three places for $20,000 (4 marks)
Sample response. (a) Savings 4% taxable at 32.5%: net = 20,000 × 0.04 × (1 − 0.325) = 20,000 × 0.04 × 0.675 = $540/yr. (b) Mathematically identical — both subtract from the interest-bearing balance, saving 20,000 × 0.05 = $1,000/yr tax-free. Offset is more accessible (everyday transaction account); redraw requires a withdrawal request. (c) Ranking by after-tax annual return: Offset = Redraw ($1,000/yr) > Savings ($540/yr).
Marking notes. 1 mark — correct after-tax savings figure $540. 1 mark — explicit "same mathematical saving" claim. 1 mark — accessibility distinction. 1 mark — correct ranking with offset and redraw tied.
2.1 — $50,000 inheritance, four options (8 marks): sample Band-6 response
Sample Band-6 response.
(a) First-year after-tax benefits.
Option W (offset): 50,000 × 0.05 = $2,500/yr tax-free interest saving.
Option X (lump-sum extra repayment): same 50,000 × 0.05 = $2,500/yr tax-free interest saving in Year 1; identical first-year benefit because both reduce the interest-bearing balance by $50,000.
Option Y (term deposit, taxed): 50,000 × 0.045 × (1 − 0.325) = 50,000 × 0.045 × 0.675 = $1,518.75/yr.
Option Z (shares, untaxed assumption): 50,000 × 0.06 = $3,000/yr expected.
[4 marks]
(b) Ranking. Z > W = X > Y. Dollar gap Z − Y = 3,000 − 1,518.75 = $1,481.25/yr. [2 marks]
(c) W vs X — same number, different reality. In Year 1, Options W and X both prevent the loan from accruing interest on $50,000 — an identical $2,500 saving at the 5% loan rate. The difference appears in everything else: with W (offset), the $50,000 remains in a transaction account, instantly accessible if an emergency or opportunity arises; with X (lump-sum repayment), the cash is gone from the borrower's reach unless the loan also has a redraw facility. Both options also compound over the life of the loan — every year the balance is smaller, less interest is charged, and more of each scheduled repayment attacks principal — so the cumulative interest saving over 30 years is far larger than the simple year-one figure suggests (commonly in the $100,000+ range for a $50,000 extra payment on a $400,000 / 5% / 30-year loan). [2 marks]
Total: 8/8.
Band descriptors for marker.
Band 3: Two of four annual benefits correct, no comparison of W vs X. ≈ 3-4 marks.
Band 4: All four annual benefits correct, ranking correct but tied W = X not explicitly identified. Part (c) restates "offset is better than savings" without analysing W vs X. ≈ 5-6 marks.
Band 5: All correct including W = X tie, dollar gap correct, Part (c) identifies same first-year benefit but does not address compounding over the loan life. ≈ 6-7 marks.
Band 6: Full numerical analysis, correct ranking with tie, and Part (c) addresses accessibility, reversibility, and the long-term compounding effect on the loan principal. 8/8.