Question 1 OR (b)
Deposit for a perpetual return
5 marks
- Time to write
- About 10 minutes
- Topic
- Time value of money
Question
Question 1 OR (b) · 5 marksA finance company makes an offer to deposit an amount of ₹13200 and then receive a return of ₹960 p.a. perpetually. Should this offer be accepted at an interest rate of 8%? Will the decision change if the interest rate is 6%?
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
- Should…?Will…?Two asks in one question: answer both.
- Should this offer…?A yes-or-no question: answer it in your first line, then explain why.
What the paper leaves open
The offer is read as: you deposit the sum with the finance company and receive the stated return every year for ever.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Perpetuity formula 1 mark 2 min
- 2 Value and decision at 8% 2 marks 3 min
- 3 Value and decision at 6% 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 3's one-line decision, whatever happens: never leave the figures without it.
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.
Reading (paper note). You deposit ₹13,200 with the company and receive ₹960 at the end of every year for ever.
A constant sum received every year for ever is a perpetuity; its present value is the annual sum divided by the rate: PV = C ÷ r. This is the same zero-growth formula used to value a share paying a constant dividend for ever, P = D ÷ Ke.
| At 8% | At 6% | |
|---|---|---|
| Present value of ₹960 a year for ever (960 ÷ r) | 12,000 | 16,000 |
| Amount to be deposited | 13,200 | 13,200 |
| Gain (loss) in present value | (1,200) | 2,800 |
| Decision | Reject | Accept |
At 8% the return is worth only ₹12,000 today, less than the ₹13,200 deposited, so the offer should be rejected. At 6% the same return is worth ₹16,000, more than the deposit, so the decision changes: accept.
Put another way, the offer yields 960 ÷ 13,200 = 7.27% a year: worth taking when money otherwise earns 6%, not when it earns 8%.
Where the 5 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Perpetuity formula | 1 |
| 2 | Value and decision at 8% | 2 |
| 3 | Value and decision at 6% | 2 |
| Total | 5 |
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