• anonymous
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?
  • Stacey Warren - Expert
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  • anonymous
k thanks
  • kropot72
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.

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