Question

The compound interest on a certain sum for 2 years is Rs 412 and the simple interest is Rs 400. What is the rate of interest per annum?

Answer 1

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Answer 2

k thanks

Answer 3

Let P be the principal and r be the rate of interest per annum expressed as a decimal.
The amount of simple interest is given by
\[400=2\Pr\ ...........(1)\]
Rearranging equation (1) to give the principal in terms of r gives:
\[P=\frac{400}{2r}\ ..........(2)\]
The amount of compound interest is given by
\[412=P(1+r)^{2}-P=P[(1+r)^{2}-1]\ .......(3)\]
Substituting the value for P from equation (2) into equation (3) gives
\[412=\frac{400}{2r}[(1+r)^{2}-1]\ .......(4)\]
Rearranging the right hand side of equation (4) to remove the inner parenthesis gives
\[412=\frac{400}{2r}(2r+r ^{2})\ ..........(5)\]
Now just solve equation (5) to find r, the decimal rate of interest.