Question 1 OR (b)
Amount to invest today for a future purchase
4 marks
- Time to write
- About 8 minutes
- Topic
- Time value of money
Question
Question 1 OR (b) · 4 marksRitika intends to buy a new mobile phone 5 years from now, and the expected price of the phone then is Rs. 120,000. At an annual interest rate of 8%, how much should Ritika invest today to have this amount in 5 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
Read from the question
- how muchFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
The amount is printed with international digit grouping, which is kept.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Present value formula and factor 2 marks 3 min
- 2 Amount to invest 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 8 minutes for 4 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 ₹1,20,000 due in 5 years at 8%: P = A ÷ (1 + i)ⁿ. The present value factor at 8% for 5 years is 0.681.
| ₹ | |
|---|---|
| Price of the phone after 5 years | 1,20,000 |
| Present value factor, 8%, 5 years | 0.681 |
| Amount to invest today | 81,720 |
Ritika should invest about ₹81,720 today. (With the unrounded factor, 1,20,000 ÷ 1.08⁵ = ₹81,669.98.)
Where the 4 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Present value formula and factor | 2 |
| 2 | Amount to invest | 2 |
| Total | 4 |
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