The compound interest on a certain sum for 2 years is {Rs. 41.60} and the simple interest is {Rs. 40.} Find the sum.

Correct Answer is : Rs. 250{Rs.~250}Rs. 250

Correct Answer is : Rs. 250{Rs.~250}Rs. 250

Test Index

Time Value of Money

Question : 39 of 99

Marks: +1, -0

\text{Rs. 41.60}

\text{Rs. 40.}

Find the sum.

Solution:

Concept:

The difference between compound interest (CI) and simple interest (SI) for 2 years is due to interest on the first year's interest.

Explanation:

Let the principal be

P

and rate be

r\%

per annum.

SI for 2 years:

\frac{P \times r \times 2}{100} = \frac{2Pr}{100} = 40

. So

Pr = 2000

CI for 2 years:

P\left(1+\frac{r}{100}\right)^2 - P = P\left(2\frac{r}{100} + \frac{r^2}{10000}\right) = \frac{2Pr}{100} + \frac{Pr^2}{10000}

Substitute

Pr = 2000

: CI

= 40 + \frac{2000 \cdot r}{10000} = 40 + \frac{r}{5}

Given CI

= 41.60

, so

40 + \frac{r}{5} = 41.60 \implies \frac{r}{5} = 1.60 \implies r = 8\%

Then

P = \frac{2000}{r} = \frac{2000}{8} = 250

Answer:

\text{Rs. 250}

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