Home-Loan Prepayment: Reduce Tenure or Reduce EMI
A bank officer is advising a home-loan customer who borrowed ₹40,00,000 at 8.5% per annum for 20 years on a monthly reducing-balance basis. The EMI has been paid regularly for 60 months. The customer receives a bonus of ₹5,00,000 and wants to prepay it immediately, with no prepayment penalty. The bank offers two options: Option A, keep the EMI unchanged and reduce the remaining tenure; Option B, keep the original 20-year tenure and reduce the EMI. The customer's current monthly surplus is tight, but he expects a salary increase next year. The officer must quantify the interest saving under both options and recommend one, also noting the liquidity risk if the bonus is used entirely for prepayment. The customer has an emergency fund of only one month's expenses. Assume the rate remains unchanged and ignore taxes.
1. Compute the EMI and the outstanding balance after 60 months.
Read the worked answer
Monthly rate r = 8.5%/12 = 0.00708333; n = 240.
EMI = P × r × (1+r)^n / [(1+r)^n − 1] (1+r)^240 ≈ 5.4412 EMI = 40,00,000 × 0.00708333 × 5.4412 / 4.4412 ≈ ₹34,712.
Outstanding after 60 months: (1+r)^60 ≈ 1.52735 Balance = P(1+r)^60 − EMI × [((1+r)^60 − 1)/r] = 40,00,000 × 1.52735 − 34,712 × (0.52735/0.00708333) ≈ 61,09,400 − 25,84,200 ≈ ₹35,25,200 (about ₹35.25 lakh).
So the prepayment reduces principal to about ₹30,25,200.
2. Compare the interest saved under Option A and Option B, and recommend one.
Read the worked answer
Option A - keep EMI ₹34,712, reduce tenure New principal = ₹30,25,200. New remaining tenure n is found from: n = −ln[1 − (r × P)/EMI] / ln(1+r) r × P = 0.00708333 × 30,25,200 ≈ ₹21,429 21,429/34,712 ≈ 0.6173; 1 − 0.6173 = 0.3827; −ln(0.3827) ≈ 0.9605 n ≈ 0.9605/0.007058 ≈ 136 months. Total remaining outflow = 34,712 × 136 + 5,00,000 ≈ ₹47,24,000 + ₹5,00,000 = ₹52,24,000. Without prepayment, remaining outflow = 34,712 × 180 ≈ ₹62,48,000. Interest saved ≈ ₹10,24,000.
Option B - keep 180 months, reduce EMI New EMI = 30,25,200 × 0.00708333 × (1.00708333)^180 / [(1.00708333)^180 − 1] (1.00708333)^180 ≈ 3.5633 New EMI ≈ ₹29,789. Total outflow = 34,712 × 60 + 29,789 × 180 + 5,00,000 ≈ ₹20,82,720 + ₹53,62,020 + ₹5,00,000 = ₹79,44,740. Original total outflow = 34,712 × 240 ≈ ₹83,30,880. Interest saved ≈ ₹3,86,000.
Recommendation: Option A saves about ₹10.24 lakh, versus about ₹3.86 lakh under Option B, so it is financially superior if the customer can sustain the current EMI. However, the customer's surplus is tight and his emergency fund is only one month. Using the entire bonus for prepayment would leave him exposed to a medical or job shock. A balanced approach is to prepay a portion - say ₹3–4 lakh - under Option A and retain ₹1–1.5 lakh as an emergency buffer, then revisit prepayment after the salary increase. If liquidity is the priority, Option B lowers the EMI by about ₹4,923 per month, but at a much higher interest cost.
3. Suppose the customer can prepay only ₹3,00,000. Recalculate the approximate interest saving under Option A and explain how the recommendation changes.
Read the worked answer
New principal after ₹3,00,000 prepayment = 35,25,200 − 3,00,000 = ₹32,25,200.
Option A keeps EMI at ₹34,712. New tenure: r × P = 0.00708333 × 32,25,200 ≈ ₹22,845 22,845/34,712 ≈ 0.6581; 1 − 0.6581 = 0.3419; −ln(0.3419) ≈ 1.0733 n ≈ 1.0733/0.007058 ≈ 152 months. Total remaining outflow = 34,712 × 152 + 3,00,000 ≈ ₹52,76,224 + ₹3,00,000 = ₹55,76,224. Without prepayment: ₹62,48,000. Interest saved ≈ ₹6,71,776.
So a ₹3 lakh prepayment still saves roughly ₹6.7 lakh under Option A - more than the ₹3.86 lakh saved by a ₹5 lakh prepayment under Option B. The recommendation becomes stronger: the customer should retain a liquidity buffer and still choose tenure reduction, because even a partial prepayment under Option A outperforms the full-bonus EMI-reduction option on interest cost. The officer should quantify the emergency-fund gap and document the customer's informed choice.