Question 1 OR (b)

Annual saving needed to reach ₹24,00,000 in five years

3 marks

Time to write: About 6 minutes
Topic: Time value of money

Question

Question 1 OR (b) · 3 marks

You intend to go abroad for higher education after working for the next five years, and you understand that ₹24,00,000 will be required for this purpose at that time. You have decided to build up this amount by investing a fixed sum at the end of each year in a safe scheme that offers interest at a rate of 10%. What amount should you invest each year to reach the target amount?

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

6 minfor 3 marks

Write it in this order

1 Sinking-fund formula 1 mark 2 min
2 Annual amount computed 2 marks 4 min

Try it first. About 6 minutes for 3 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 deposits are equal and made at the end of each year, so they form an annuity whose future value must equal the target: Sn = A × FVIFA(i, n), so A = Sn ÷ FVIFA(10%, 5).

FVIFA(10%, 5) = (1.10⁵ − 1) ÷ 0.10 = 6.1051 (6.105 in the table).
Annual deposit = 24,00,000 ÷ 6.1051 = ₹3,93,113.95.

Check: 3,93,113.95 × (1.4641 + 1.331 + 1.21 + 1.10 + 1) = 3,93,113.95 × 6.1051 = ₹24,00,000.

You should invest about ₹3,93,114 at the end of each year. (With the table value 6.105, ₹3,93,120.)

Where the 3 marks sit

#	Component	Marks
1	Sinking-fund formula	1
2	Annual amount computed	2
	Total	3

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