Question 1 (b)
Present value of a sum needed in four years
3 marks
- Time to write
- About 6 minutes
- Topic
- Time value of money
Question
Question 1 (b) · 3 marksIf you wish to accumulate ₹60,000 in four years and are able to earn an interest rate of 8%, how much should you invest today?
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
- how muchFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- 1 Present value formula and factor 1 mark 2 min
- 2 Amount to invest today 2 marks 4 min
Try it first. About 6 minutes for 3 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 amount to invest today is the present value of ₹60,000 receivable after 4 years, discounted at 8%: P = A ÷ (1 + i)ⁿ, where A is the future sum, i the rate and n the number of years. Present value tables give the factor 1 ÷ (1 + i)ⁿ directly; at 8% for 4 years it is 0.735.
| ₹ | |
|---|---|
| Sum required after 4 years (A) | 60,000 |
| Present value factor, 8%, 4 years | 0.735 |
| Amount to invest today (60,000 × 0.735) | 44,100 |
Invested today at 8% compound interest, about ₹44,100 grows to ₹60,000 in four years. (With the unrounded factor, 60,000 ÷ 1.08⁴ = ₹44,101.79.)
Where the 3 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Present value formula and factor | 1 |
| 2 | Amount to invest today | 2 |
| Total | 3 |
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