The Extra Repayment Trade-off
Priya takes out a home loan of $420,000 at a nominal annual interest rate of 4.8% compounding monthly, over 30 years, with monthly repayments. She is offered two strategies. Strategy A: pay exactly the required monthly repayment for the full term. Strategy B: pay an extra $250 per month from the start and keep the same repayment amount even when the bank recalculates. Priya's bank charges no fees for extra repayments, but she must keep $15,000 in an offset account earning 0% toward the loan for emergencies; money in the offset account reduces the interest charged on the loan balance. Priya earns 3.2% per annum on savings outside the offset account. She plans to sell the property after 8 years.
1. Calculate the required monthly repayment under Strategy A, and determine the loan balance owing after 8 years (96 repayments). Show the recursion or formula you use and give values to the nearest dollar.
Read the worked answer
Monthly rate i = 0.048/12 = 0.004. Number of repayments n = 360.\n\nRepayment R = P·i / (1 − (1+i)^(−n))\n= 420000 × 0.004 / (1 − 1.004^(−360)).\n1.004^(−360) ≈ 0.23719, so denominator ≈ 0.76281.\nR ≈ 1680 / 0.76281 ≈ $2,202 per month.\n\nBalance after 96 payments: B = P(1+i)^96 − R[((1+i)^96 − 1)/i].\n1.004^96 ≈ 1.4673.\nP(1+i)^96 ≈ 420000 × 1.4673 ≈ $616,266.\nR × ((1.4673 − 1)/0.004) ≈ 2202 × 116.83 ≈ $257,258.\nB ≈ 616266 − 257258 ≈ $359,008.\n\nSo Priya still owes roughly $359,000 after 8 years, having repaid about $211,000 in cash but reduced principal by only about $61,000.
2. Compare the two strategies at the 8-year sale point, taking the offset account into account. Which strategy leaves Priya financially better off, and by roughly how much? State any assumptions.
Read the worked answer
Under Strategy B she repays R + 250 = $2,452 per month.\nBalance after 96 payments: B = 420000(1.004)^96 − 2452 × 116.83.\n= 616266 − 286,467 ≈ $329,799.\n\nExtra principal cleared compared with Strategy A: 359,008 − 329,799 ≈ $29,209.\nCash paid extra over 8 years: 250 × 96 = $24,000.\n\nAt first glance Strategy B looks only marginally better because $24,000 extra cash cleared $29,209 of principal - a gain of about $5,200 from avoided interest.\n\nBut the offset account matters. If Priya keeps $15,000 in the offset for the whole 8 years, interest is charged on (balance − 15,000). The interest saved is approximately 15,000 × 0.004 × 96 ≈ $5,760 in simple terms (compounding makes it slightly more). This benefit is available under either strategy, so it does not change the ranking, but it means Priya should not drain the offset to fund the extra repayments.\n\nStrategy B is better by roughly $5,200 in interest avoided, provided the $250 comes from income rather than from the offset account. If she instead withdrew $250/month from the offset, she would lose the offset benefit on that money, roughly cancelling the gain. Assumption: interest rate stays at 4.8% for 8 years and she sells at exactly 96 months.
3. Priya could instead direct the $250/month into a savings account earning 3.2% per annum compounding monthly. Evaluate whether this beats the extra-repayment strategy over the 8 years, and explain the judgement call.
Read the worked answer
Future value of $250/month at 0.032/12 = 0.0026667 per month over 96 months:\nFV = 250 × ((1.0026667)^96 − 1)/0.0026667.\n1.0026667^96 ≈ 1.2910.\nFV ≈ 250 × (0.2910/0.0026667) ≈ 250 × 109.13 ≈ $27,283.\n\nCompare with the loan-side benefit. The extra repayments saved about $29,209 of principal over the same period (from Task 2), which is more than $27,283. The loan rate (4.8%) exceeds the savings rate (3.2%), so repaying the loan wins on pure numbers.\n\nJudgement call: the margin is only about $1,900 over 8 years, and the savings option keeps the money liquid. If Priya might need cash before selling, or if the loan has a redraw facility, the flexibility may be worth more than $1,900. Conversely, if she is confident she will not need the cash, extra repayments are the better financial choice. The key insight is that the comparison depends on the rate differential, not on the size of the repayments, and the offset account already provides liquidity, so the extra-repayment strategy is defensible.