Question 1 (b)
Deposit today for two future sums
4 marks
- Time to write
- About 8 minutes
- Topic
- Time value of money
Question
Question 1 (b) · 4 marksMr. Rakesh has received a huge amount of salary arrears. He wishes to invest part of the arrears for his children's higher studies. For this purpose he needs Rs. 1,80,000 for his son and Rs. 2,04,000 for his daughter, after 5 years and 7 years respectively. Find out the deposit which, if invested @. 10% p.a., will produce these future cash inflows.
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
- Find outFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
"@. 10%" is printed so and kept.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Present value formula and factors 1 mark 2 min
- 2 Present value of each sum 2 marks 3 min
- 3 Total deposit 1 mark 2 min
Short on time? Step 2 carries 2 of the 4 marks: guard its minutes.
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 deposit needed today is the present value of the two future sums at 10%: P = A ÷ (1 + i)ⁿ, with the factors taken from the present value table.
| Purpose | Amount needed (₹) | After (years) | PV factor @ 10% | Present value (₹) |
|---|---|---|---|---|
| Son's studies | 1,80,000 | 5 | 0.621 | 1,11,780 |
| Daughter's studies | 2,04,000 | 7 | 0.513 | 1,04,652 |
| Deposit required today | 2,16,432 |
Mr. Rakesh should deposit about ₹2,16,432 today at 10%. (With unrounded factors, 1,80,000 ÷ 1.1⁵ + 2,04,000 ÷ 1.1⁷ = ₹2,16,450.)
Where the 4 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Present value formula and factors | 1 |
| 2 | Present value of each sum | 2 |
| 3 | Total deposit | 1 |
| Total | 4 |
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