Question 1 OR (b)
Present value of a future sum
7 marks
- Time to write
- About 14 minutes
From an older CBCS paper
Question
Question 1 OR (b) · 7 marksThe cost of a new mobile phone is Rs. 12,000. At an interest rate of 5%, how much would you need to set aside now to have this sum in five years? 7
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
- Read the data; note exactly what is asked 1 min
- 1 Present value concept and formula 3 marks 5 min
- 2 Factor and amount 4 marks 7 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 14 minutes for 7 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. Money has time value, so a sum needed in the future is worth less today; the amount to set aside now is its present value, the future sum multiplied by the present value factor 1 ÷ (1 + i)ⁿ. The present value approach is the exact opposite of compounding: money received in the future is discounted back to today.
Calculation. Present value factor for 5 years at 5% = 1 ÷ (1.05)⁵ = 0.784 (table).
Amount to set aside now = 12,000 × 0.784 = ₹9,408.
(With the unrounded factor, 0.78353, the amount is ₹9,402.31.) Invested at 5% compound interest, ₹9,408 grows to about ₹12,000 in five years, the cost of the phone.
Where the 7 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Present value concept and formula | 3 |
| 2 | Factor and amount | 4 |
| Total | 7 |
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