Test Index

Time Value of Money

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Question : 37 of 99

Marks: +1, -0

\mathrm{Rs.}\,2,000

is invested at annual rate of interest of

10\%

p.a. The amount after two years if compounding is done half yearly, is -

$\text{Rs.}\,2431$
$\text{Rs.}\,243.10$
$\text{Rs.}\,2341$
None

Solution:

Concept:

Half-yearly compounding means number of compounding periods doubles and the rate is halved.

Explanation:

Principal

P = \text{Rs.}2000

, annual rate

R = 10\%

, so half-yearly rate

r = \frac{10}{2} = 5\%

per half-year.

Number of half-years in 2 years:

n = 2 \times 2 = 4

.

Amount formula:

A = P \left(1 + \frac{r}{100}\right)^n = 2000 \left(1 + \frac{5}{100}\right)^4 = 2000 \times (1.05)^4

.

Compute:

(1.05)^2 = 1.1025

, then

(1.1025)^2 = 1.21550625

.

A = 2000 \times 1.21550625 = 2431.0125 \approx \text{Rs.}2431

.

Answer:

The amount after two years is

\text{Rs. }2431

.

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