Test Index

Time Value of Money

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Question : 45 of 99

Marks: +1, -0

The future value of an annuity of

\text{Rs.}\,1,000

made annually for 5 years at the rate of interest

14\,\%

compound annually is

$\text{Rs.}\,5610$
$\text{Rs.}\,6610$
$\text{Rs.}\,6160$
$\text{Rs.}\,5160$

Solution:

Concept:

Future value of an annuity:

FV = P \times \frac{(1+r)^n - 1}{r}

, where

P

is periodic payment,

r

is rate per period,

n

is number of periods.

Explanation:

Given:

P = 1000

,

r = 14\% = 0.14

,

n = 5

.

Compute

(1.14)^5

:

(1.14)^2 = 1.2996

,

(1.14)^4 = (1.2996)^2 \approx 1.6889

, then multiply by

1.14

gives

1.6889 \times 1.14 \approx 1.9254

.

Now,

(1.9254 - 1) = 0.9254

.

Divide by

0.14

:

\frac{0.9254}{0.14} = 6.61

(approx).

Multiply by

1000

:

FV = 1000 \times 6.61 = 6610

.

Answer:

\text{Rs.}\,6610

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