Test Index

Time Value of Money

Question : 10 of 99

Marks: +1, -0

7\%

\text{₹}\,50000

for retirement at the age of 60 .

Solution:

Concept:

Find the present value of a future lump sum using compound interest formula.

Explanation:

Let

P

be the present value.

Rate

r = 7\% = 0.07

, compounded semi-annually so

n = 2

Time

t = 30

years (age 30 to 60).

Number of periods

N = n \times t = 2 \times 30 = 60

Rate per period

i = \frac{r}{n} = \frac{0.07}{2} = 0.035

Future value

FV = \text{₹}\,50000

Present value formula:

P = \frac{FV}{(1 + i)^N}

Thus

P = \frac{50000}{(1.035)^{60}}

Compute

(1.035)^{60} \approx 7.878

P = \frac{50000}{7.878} \approx 6346.7

Answer:

The amount to invest now is approximately

\text{₹}\,6346.7

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