Question 1 (b)
Equal annual withdrawal over 15 years
5 marks
- Time to write
- About 10 minutes
- Topic
- Time value of money
Question
Question 1 (b) · 5 marksAn investor places a sum of ₹2,40,000 in a bank account that credits interest @ 10% p.a. What amount can be withdrawn annually over a period of 15 years?
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Deposit as the present value of an annuity 2 marks 3 min
- 2 Annuity factor and withdrawal 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 10 minutes for 5 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
The ₹2,40,000 deposited now is the present value of the 15 equal withdrawals at 10%, so each withdrawal is the deposit divided by the present value annuity factor: PVA = A × annuity discount factor, so A = 2,40,000 ÷ PVAF(10%, 15). The annuity factor is the sum of the yearly present value factors.
- PVAF(10%, 15) = [1 − 1.10⁻¹⁵] ÷ 0.10 = 7.6061.
- Annual withdrawal = 2,40,000 ÷ 7.6061 = ₹31,553.71.
Check: the account, credited with 10% interest each year and drawn ₹31,553.71 at each year-end, is exhausted after the 15th withdrawal. (With the 3-decimal table factor 7.606, about ₹31,554.)
Where the 5 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Deposit as the present value of an annuity | 2 |
| 2 | Annuity factor and withdrawal | 3 |
| Total | 5 |
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