Test Index

Time Value of Money

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Question : 19 of 99

Marks: +1, -0

If the compound interest on a certain sum for 2 years at

3 \%

\text{Rs. 101.50}

. what would be the S.I.?

$\text{Rs.} 100$
$\text{Rs.}200$
$\text{Rs.} 300$
None

Solution:

Concept:

Use the relationship between compound interest (CI) and simple interest (SI) for 2 years.

Explanation:

Let the principal be

P

.

CI for 2 years at

3\%

:

P\left[\left(1+\frac{3}{100}\right)^2 - 1\right] = 101.50

.

Compute:

\left(1.03^2-1\right) = 1.0609-1 = 0.0609

.

So

P \times 0.0609 = 101.50 \implies P = \frac{101.50}{0.0609}

.

Simplify:

\frac{101.50}{0.0609} = \frac{1015000}{609} = \frac{5000}{3}

(since

1015000 \div 203 = 5000

,

609 \div 203 = 3

).

Thus

P = \frac{5000}{3}

.

SI for 2 years at

3\%

:

\frac{P \times 3 \times 2}{100} = \frac{\frac{5000}{3} \times 6}{100} = \frac{5000 \times 6}{300} = \frac{30000}{300} = 100

.

Answer:

Rs. 100

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