Comparing Fixed Deposits When Early Withdrawal Is Possible
A retired teacher has ₹75,000 to deposit for 2 years. Bank P offers 8.4% per annum simple interest. Bank Q offers 8% per annum compounded annually. Bank R offers 7.8% per annum compounded half-yearly. If the deposit is withdrawn after 18 months, Bank P pays only 4% simple interest for the actual period, Bank Q pays 6.5% simple interest for the completed months, and Bank R pays 6% simple interest for the completed months. The teacher expects to complete the full 2 years but may need the money earlier for a family medical expense. She wants the highest full-term maturity but does not want to lose a large amount if her plans change. A friend tells her to choose Bank P only because 8.4% is the highest quoted rate.
1. Calculate the maturity amount after 2 years for each bank and rank them.
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Bank P, simple interest: I = 75000 × 8.4 × 2 ÷ 100 = ₹12,600. Amount = 75,000 + 12,600 = ₹87,600. Bank Q, compounded annually: Amount = 75,000 × (1.08)² = 75,000 × 1.1664 = ₹87,480. Bank R, compounded half-yearly: Half-yearly rate = 7.8 ÷ 2 = 3.9%; number of periods = 4. Amount = 75,000 × (1.039)⁴ ≈ 75,000 × 1.165366 = ₹87,402.43. Ranking: P ₹87,600 > Q ₹87,480 > R ₹87,402.43. P is highest, but only ₹120 above Q.
2. Calculate the amount payable after 18 months if the teacher withdraws early from Bank P and Bank Q. Which pays more in that case?
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18 months = 1.5 years. Bank P at 4% simple: I = 75000 × 4 × 1.5 ÷ 100 = ₹4,500. Amount = ₹79,500. Bank Q at 6.5% simple: I = 75000 × 6.5 × 1.5 ÷ 100 = ₹7,312.50. Amount = 75,000 + 7,312.50 = ₹82,312.50. Bank Q pays 82,312.50 − 79,500 = ₹2,812.50 more than Bank P on early withdrawal. Bank R would pay 75,000 + (75000 × 6 × 1.5 ÷ 100) = ₹81,750, also more than P.
3. Advise the teacher. How certain must she be of completing 2 years before Bank P becomes the better choice?
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Bank P's full-term gain over Bank Q is only ₹120. If she withdraws at 18 months, Bank P loses ₹2,812.50 compared with Bank Q. Let p be the probability she completes 2 years. P is better when: p × 120 > (1 − p) × 2812.50. 120p > 2812.50 − 2812.50p 2932.50p > 2812.50 p > 2812.50 ÷ 2932.50 ≈ 0.959. She must be about 96% certain of completing the full term for P's tiny extra ₹120 to justify the much lower early-withdrawal payout. Unless she is almost certain, Bank Q is the safer choice; if full-term certainty is very high, Bank P gives the highest maturity.