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The compound interest on a certain sum for 2 years is Rs.2520 and simple interest on the same sum of money at same rate of interest for 2 years is Rs.2400. Find the sum and rate of interest.

(a) Rs.12000, 10%  (b) Rs.18000, 6%

(c) Rs.13600, 12%  (d) Rs.24000, 5%

1 Answer

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In simple interest, interest is calculated on principal amount. Let $S$ be the principal amount.

$$\begin{equation} S \times r \times 2=2400\label{ref1} \end{equation}.$$

The simple interest for 1 year is 2400/2 = 1200.

For compound interest, interest is paid on this interest also and the difference of SI and CI for 2 years will be exactly this interest for 1200.

So, $$\begin{equation} 1200 \times r = 2520 - 2400 = 120 \\ \implies r = 0.1\label{ref2}\end{equation}.$$

From $\ref{ref1}$ and $\ref{ref2}$

$S = \frac{2400}{2 \times 0.1} = 12000$.

So, a choice.
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