Three Deposit Schemes, One Property Payment at Month 18
A customer has Rs 4,00,000 to place for two years and is comparing three deposits at your branch. Scheme P pays 8.5% p.a. compounded annually, with principal and interest paid at maturity; if she closes it at 18 months, the entire period is re-rated at 6.5% p.a. simple. Scheme Q pays 8.25% p.a. compounded quarterly and may be closed at 18 months, but a penalty of 0.5% of the principal is deducted on any closure before 24 months. Scheme R pays 8.75% p.a. simple, with interest credited to her savings account every quarter, and carries no penalty on closure; she does not reinvest the quarterly interest. She expects a property payment at month 18 and puts the chance of needing the money then at "about one in three". The branch's tax desk has told her that TDS at 10% will be deducted on interest credited in a financial year above Rs 50,000, whichever scheme she picks.
1. Compute the amount she receives at the end of two years under each scheme if she does not touch the money, rank them, and say whether the ranking is a meaningful basis for a decision.
Read the worked answer
- P: 4,00,000 × 1.085² = 4,00,000 × 1.177225 = Rs 4,70,890.
- Q: quarterly rate 8.25/4 = 2.0625%; 4,00,000 × 1.020625⁸ = 4,00,000 × 1.177419 = Rs 4,70,968.
- R: 4,00,000 + 4,00,000 × 8.75% × 2 = 4,00,000 + 70,000 = Rs 4,70,000.
Ranking: Q (Rs 4,70,968) > P (Rs 4,70,890) > R (Rs 4,70,000).
Q's lead over P is Rs 78 - under 0.02% of the principal, and smaller than one day's delay in crediting. It is not a basis for a decision; it is rounding noise dressed up as a result. The real spread is Q's Rs 968 over R, which is also trivial at maturity. The decision has to be made on what happens at month 18, not at month 24.
The TDS warning turns out to be irrelevant to the comparison: P credits about Rs 34,000 and Rs 36,890 in the two years, Q similar, R Rs 35,000 a year - none crosses Rs 50,000, so no scheme is disadvantaged, and TDS is in any case the customer's own tax paid early, not a cost.
2. Compute the month-18 exit value of each scheme, then use her one-in-three estimate to decide which scheme she should choose.
Read the worked answer
Exit at 18 months:
- P: re-rated at 6.5% simple for 1.5 years - 4,00,000 × (1 + 0.065 × 1.5) = 4,00,000 × 1.0975 = Rs 4,39,000.
- Q: six quarters - 4,00,000 × 1.020625⁶ = Rs 4,52,123, less penalty 0.5% of 4,00,000 = Rs 2,000 → Rs 4,50,123.
- R: six quarterly credits of Rs 8,750 = Rs 52,500, no penalty → Rs 4,52,500.
P is dominated: it loses to Q in both states (Rs 4,39,000 against Rs 4,50,123 early; Rs 4,70,890 against Rs 4,70,968 late). Drop it.
Expected value (p = chance of exit at month 18):
- Q: ⅔ × 4,70,968 + ⅓ × 4,50,123 = Rs 4,64,020.
- R: ⅔ × 4,70,000 + ⅓ × 4,52,500 = Rs 4,64,167.
R edges ahead. Find the break-even: Q − R = 968 − 3,345p, which is zero at p ≈ 0.29. Above a 29% chance of needing the money at month 18, R wins; below it, Q wins. Her one-in-three (33%) is just past the threshold, so R is the choice - but the honest answer is that the margin is Rs 147 and the estimate of p is a guess, so the decision should lean on certainty, not arithmetic.
3. Write the recommendation you would actually give at the counter, including the non-numeric factors that should override the Rs 147 difference.
Read the worked answer
Recommend R, and say why in the customer's terms: she keeps every rupee of interest she has already earned, she pays no penalty for the property payment she half-expects, and she gives up roughly Rs 970 at most if she never touches the money. Against that, Q pays about Rs 150 more in expectation but only if her one-in-three estimate is roughly right, and it punishes her if she is wrong about the timing.
Factors that matter more than the Rs 147:
- Penalty base. Q's penalty is 0.5% of principal - a fixed Rs 2,000 hit, not a slice of interest, so it bites hardest if she exits early in the term.
- Reinvestment risk on R. The quarterly interest lands in a savings account at whatever rate prevails; if she spends it rather than reinvesting, R's effective return falls below the quoted 8.75%.
- Reinvestment risk on Q. At maturity she faces the same rate decision in two years; locking 8.25% quarterly compounding is not the same as guaranteeing a rate for longer.
- Certainty and liquidity. She has a dated obligation. A scheme that lets her meet it without a penalty is worth more than Rs 147 of expected value.
Close by noting that the ranking of headline rates - 8.75% > 8.5% > 8.25% - is misleading here, because the rates are on different compounding bases and one is paid out rather than accumulated.