Two Deposit Routes and the Break-Even Reinvestment Rate
A customer walks into the branch with ₹2,50,000 and asks the clerk to compare two fixed deposit routes before she signs the application. Option A is a two-year deposit at 7.25% per annum compounded quarterly. Option B is a one-year deposit at 7.00% per annum compounded annually, whose maturity proceeds would then be reinvested for a second year; the branch's rate card for that tenor currently shows 7.50% per annum compounded annually, but the clerk is careful to say that this card rate is not guaranteed for a deposit opened twelve months later. In both routes interest is paid only on maturity and there is no premature withdrawal. The customer does not need the money for two years. She wants the arithmetic written out, because she is comparing the two routes on the rupee difference at the end, on the effective annual yield of each route, and on how far the second-year rate could fall before Option B stops being the better choice.
1. Compute the maturity value of each route and state the rupee difference.
Read the worked answer
Option A: the quarterly rate is 7.25 / 4 = 1.8125%, and two years means 8 compounding periods.
1.018125^8 = 1.154540 (working up in squares: 1.018125² = 1.036579, then 1.074495, then 1.154540).
Maturity = 2,50,000 × 1.154540 = ₹2,88,635 (₹2,88,634.89 exactly), so interest is about ₹38,635.
Option B: year 1 gives 2,50,000 × 1.07 = ₹2,67,500. Year 2 at the card rate of 7.50% gives 2,67,500 × 1.075 = ₹2,87,562.50, so interest is ₹37,562.50.
Difference = 2,88,634.89 − 2,87,562.50 = ₹1,072.39 in favour of Option A.
Note that quarterly compounding adds value even though the quoted rate is only 0.25 percentage points higher: the extra compounding frequency, not the headline rate, does most of the work.
2. Convert both routes into effective annual yields and advise the customer, bearing in mind that one route has a certainty the other lacks.
Read the worked answer
Option A: 1.154540^(1/2) − 1 = 1.074495 − 1 = 7.45% per annum effective.
Option B: (1.07 × 1.075)^(1/2) − 1 = (1.15025)^(1/2) − 1 = 1.072497 − 1 = 7.25% per annum effective.
The geometric mean of 7.00% and 7.50% is slightly below their arithmetic average of 7.25%, which is why Option B's effective yield sits just under 7.25%.
Advice: Option A is better on both counts. It yields about 20 basis points more per year and it is locked in at the time of booking, whereas Option B depends on a card rate that may not exist next year. The rupee gain is small, only about ₹1,072 over two years, so the customer should not be pushed on the arithmetic alone; but since she does not need the money for two years, there is no liquidity reason to prefer the one-year route. A clerk should present Option A as the recommendation and show Option B as the benchmark it beats.
3. At what second-year rate would Option B merely equal Option A, and what does that tell the customer about the risk she is taking?
Read the worked answer
Set the year-2 multiplier equal to the ratio of the two maturity values.
Required factor = 2,88,634.89 / 2,67,500 = 1.079008.
So the required second-year rate is 7.9008%, that is about 7.90% per annum, not the 7.50% on today's card.
Check: 2,67,500 × 1.079008 = ₹2,88,634.6, which matches Option A within rounding.
Interpretation: Option B only wins if the one-year rate rises by about 40 basis points in twelve months, to more than 7.90%. The customer would be taking a reinvestment bet to earn, at best, the same ₹2,88,635 she can lock in today. Downside matters more than upside here: if the rate falls to 7.00%, Option B matures at 2,67,500 × 1.07 = ₹2,86,225, roughly ₹2,410 below Option A. The correct branch response is to quote the break-even rate openly rather than to project a future card rate as if it were assured.