Question 1 (a)
Annual saving to reach a target sum (sinking fund)
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 1 (a) · 8 marks- Pramila wants to go on a world tour after 10 years, which will cost her ₹10,20,000. How much should she save each year to have ₹10,20,000 after 10 years, at a rate of interest of 10% p.a.? If the rate of interest is 12% p.a., what will the annual amount to be saved be?
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…?Is…?Two asks in one question: answer both.
- How muchFormula first, then the working, then the answer with its unit (₹, %, units).
- should sheEnd with a one-line decision that follows from your figures.
What the paper leaves open
The savings are made at the end of each year (an ordinary annuity, C8).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Future value of an annuity: approach 2 marks 4 min
- 2 Saving at 10% 3 marks 5 min
- 3 Saving at 12% 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 16 minutes for 8 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): equal savings at the end of each year for 10 years (an ordinary annuity). Their future value must equal ₹10,20,000: future value = annual saving × FVIFA, the compound value annuity factor. So the annual saving = 10,20,000 ÷ FVIFA. Compound value grows as A = P(1 + i)ⁿ.
| Rate | FVIFA (10 years) | Annual saving (₹) |
|---|---|---|
| 10% | 15.937 | 10,20,000 ÷ 15.937 = 64,002.01 |
| 12% | 17.549 | 10,20,000 ÷ 17.549 = 58,122.97 |
Pramila must save ₹64,002.01 a year at 10%, or ₹58,122.97 a year at 12%. At the higher rate more of the target comes from compound interest, so a smaller annual saving is needed.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Future value of an annuity: approach | 2 |
| 2 | Saving at 10% | 3 |
| 3 | Saving at 12% | 3 |
| Total | 8 |
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