Choosing Between Two Term Deposits for a Senior Citizen Who May Close Early
A customer aged 61 years and 4 months visits the branch with ₹2,40,000 to place for exactly 24 months. The branch offers two term-deposit options. Scheme P pays 8.40% per annum compounded annually, with interest credited only on maturity. Scheme Q pays 8.50% per annum simple interest, and the branch's board-approved policy adds 0.50% per annum to the card rate for depositors who have completed 60 years on the date of opening the deposit. The customer has his Aadhaar card showing his date of birth but has not carried his PAN card, and he says he will bring it next week. He also mentions that if a family medical expense comes up, he may need to close the deposit after about 15 months. The branch's premature-closure clause pays 6.00% per annum simple on Scheme P and 7.00% per annum simple on Scheme Q, with no senior-citizen loading in either case, and no penalty is deducted beyond the rate cut.
1. Which scheme gives the higher maturity amount for this customer, and by how much? Show the eligibility check and the arithmetic.
Read the worked answer
Step 1 - Eligibility check first, not arithmetic. The senior-citizen loading applies to depositors who have completed 60 years on the date of opening. The customer is 61 years 4 months, so he qualifies. Scheme Q therefore carries 8.50% + 0.50% = 9.00% per annum simple. Had he been 59 years 11 months, the loading would not apply and the whole comparison would change.
Step 2 - Scheme P (compound).
- ₹2,40,000 × 1.084 = ₹2,60,160
- ₹2,60,160 × 1.084 = ₹2,82,013.44
- Interest = ₹42,013.44
Step 3 - Scheme Q (simple, with loading).
- Interest = 2,40,000 × 9% × 2 = ₹43,200
- Maturity = ₹2,83,200
Step 4 - Compare. ₹2,83,200 − ₹2,82,013.44 = ₹1,186.56.
Answer: Scheme Q is better by ₹1,186.56. The lesson is that the headline rate alone misleads: 8.40% compounded beats an unlevered 8.50% simple, but the 0.50% senior loading reverses the result. Also note the branch must not open the deposit on an oral age claim - the Aadhaar date of birth is the proof, and PAN must be obtained before the deposit is booked.
2. If the customer closes the deposit after 15 months instead of 24, which scheme pays more and by how much? State the assumption you are making about the senior-citizen loading.
Read the worked answer
Assumption stated in the setup: on premature closure, no senior-citizen loading applies to either scheme, and no penalty is charged beyond the rate cut. So the senior loading is irrelevant to this comparison - a common trap, because in the maturity comparison it was decisive.
Scheme P, 15 months at 6.00% simple:
- 2,40,000 × 0.06 × (15/12) = 2,40,000 × 0.075 = ₹18,000 interest
- Proceeds = ₹2,58,000
Scheme Q, 15 months at 7.00% simple:
- 2,40,000 × 0.07 × 1.25 = 2,40,000 × 0.0875 = ₹21,000 interest
- Proceeds = ₹2,61,000
Answer: Scheme Q pays ₹3,000 more on premature closure.
Why this matters at the counter: the customer had flagged a possible 15-month exit. Scheme Q wins on both counts here (maturity and early exit), so it is the correct recommendation with no conflict to resolve. If the early-exit rates had favoured Scheme P instead, the honest advice would be to split the money into two deposits of ₹1,20,000 each - one in each scheme - rather than guess which risk will materialise.
3. The Aadhaar card actually shows his date of birth as 8 months short of 60 years, and he had misstated his age at the counter. How does the recommendation change, and what should the clerk do before booking?
Read the worked answer
Recalculate with the loading removed. Scheme Q now pays only 8.50% per annum simple:
- Interest = 2,40,000 × 8.5% × 2 = ₹40,800
- Maturity = ₹2,80,800
Scheme P is unchanged at ₹2,82,013.44 (₹42,013.44 interest).
Difference: ₹2,82,013.44 − ₹2,80,800 = ₹1,213.44 in favour of Scheme P. The recommendation flips purely on the date-of-birth proof.
What the clerk must do:
- Treat the documentary date of birth as final; an oral statement of age has no value for rate purposes.
- Apply the rate applicable on the date of opening; if his 60th birthday falls during the tenor, the loading does not get applied mid-term unless the branch's board policy expressly allows a mid-term rate reset (most do not).
- Record the age verification in the account-opening file, and tell the customer plainly why the quoted 9.00% cannot be given.
- If he prefers to wait a few months to cross 60, show him both numbers and let him choose - do not silently book him at the lower rate or quietly promise the higher one.
Exam point: rate selection is driven by verified eligibility, and the check must be done before the arithmetic.