Question

Hasan wants to accumulate $10,000 in today’s dollars. How much does he need to pay in actual dollars at end of years 1,2,3,4 and 5 in order to accumulate the required amount?   The inflation rate is 3% and the market interest rate is 10%.

Answer 1

Real interest rate (R) should be calculated first.

R = (Nominal rate – Inflation rate) / (1 + inflation rate)

    = (0.10 – 0.03) / (1 + 0.03)

    = 0.07 / 1.03

    = 0.06796

    = 6.80

Let the amount of payment is X

Hence,

Year	CF	F = 6.80% factor = 1/1.068^year	PV = CF × F
1	X	1/1.068^1 = 0.936329	0.936329X
2	X	1/1.068^2 = 0.876713	0.876713X
3	X	1/1.068^3 = 0.820892	0.820892X
4	X	1/1.068^4 = 0.768625	0.768625X
5	X	1/1.068^5 = 0.719687	0.719687X
			Total = 4.122246X

As per the condition,

4.122246X = 10,000

X = 10,000 / 4.122246

    = $2,425.86 (Answer)