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Time Value of Money

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Question : 20 of 99

Marks: +1, -0

A sum of money is put at compound interest for 2 years at

20 \%

p.a. It would earn

\text{Rs}482

more, if the interest were payable half-yearly than it were payable yearly; then the sum is

$\text{Rs.}20,000$
$\text{₹} 25,000$
$\text{Rs.}\,26,000$
None

Solution:

Concept:

The difference in compound interest arises from the compounding frequency.

Explanation:

Let the principal be

P

.

Yearly compounding at

20\%

p.a. for 2 years:

Amount =

P(1+0.20)^2 = 1.44P

CI yearly =

1.44P - P = 0.44P

Half-yearly compounding at

10\%

per half-year for 4 half-years:

Amount =

P(1+0.10)^4 = 1.4641P

CI half-yearly =

1.4641P - P = 0.4641P

Difference =

0.4641P - 0.44P = 0.0241P = 482

So

P = \frac{482}{0.0241} = 20000

Answer:

₹20,000

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