Question 1 OR (a)
Deposit now to fund two future withdrawals
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 1 OR (a) · 8 marks- Assume that at year zero a deposit is to be made into an account earning 8%, compounded annually, so that ₹2,40,000 can be withdrawn three years from now and ₹3,60,000 seven years from now. How large must the year zero deposit be to produce these future payments?
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
Read from the question
- Assume that at year zero a…The paper fixes this: use it as given, and say so in your answer.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Approach 2 marks 3 min
- 2 Present values of the two withdrawals 4 marks 7 min
- 3 Deposit needed 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? Step 2 carries 4 of the 8 marks: guard its minutes.
Try it first. About 16 minutes for 8 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.
Approach. A sum due in the future is worth less today because money has time value. The deposit needed now is the present value, at 8%, of the two withdrawals: each future sum multiplied by its present value factor 1 ÷ (1 + i)ⁿ, and the results added.
| Withdrawal | Year | PVF @ 8% | Present value (₹) |
|---|---|---|---|
| 2,40,000 | 3 | 0.794 | 1,90,560 |
| 3,60,000 | 7 | 0.583 | 2,09,880 |
| Deposit needed at year zero | 4,00,440 |
A deposit of ₹4,00,440 now, earning 8% compounded annually, provides ₹2,40,000 at the end of year 3 and ₹3,60,000 at the end of year 7 (to within the rounding of the table factors).
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Approach | 2 |
| 2 | Present values of the two withdrawals | 4 |
| 3 | Deposit needed | 2 |
| Total | 8 |
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