Find the difference between compound interest and simple interest on Rs. 45000 at 12% p.a. for 5 years. Ans.7200
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P = ₹45000
r = 12 %
t = 5 years
![\text{Difference of CI and SI =} CI - SI \\ \\ = P{\bigg(1+\frac{r}{100}\bigg)}^t -P - \frac{Ptr}{100} \\ \\ = P\bigg[{\bigg(1+\frac{r}{100}\bigg)}^t - 1 - \frac{tr}{100} \bigg]](https://tex.z-dn.net/?f=%5Ctext%7BDifference+of+CI+and+SI+%3D%7D+CI++-++SI+%5C%5C++%5C%5C++%3D+P%7B%5Cbigg%281%2B%5Cfrac%7Br%7D%7B100%7D%5Cbigg%29%7D%5Et++-P++-+%5Cfrac%7BPtr%7D%7B100%7D+%5C%5C++%5C%5C++%3D+P%5Cbigg%5B%7B%5Cbigg%281%2B%5Cfrac%7Br%7D%7B100%7D%5Cbigg%29%7D%5Et+-+1+-+%5Cfrac%7Btr%7D%7B100%7D+%5Cbigg%5D "\text{Difference of CI and SI =} CI - SI \\ \\ = P{\bigg(1+\frac{r}{100}\bigg)}^t -P - \frac{Ptr}{100} \\ \\ = P\bigg[{\bigg(1+\frac{r}{100}\bigg)}^t - 1 - \frac{tr}{100} \bigg]")
![= 45000\bigg[{\bigg(1+\frac{12}{100}\bigg)}^5 - 1- \frac{5 \times 12}{100} \bigg]\\ \\ =45000 \big[{1.12}^5 -1 - 0.6 \big]\\ \\ =45000\big[1.76 -1.6 \big] \\ \\ = 45000 \times 0.16 \\ \\ = 7200](https://tex.z-dn.net/?f=+%3D+45000%5Cbigg%5B%7B%5Cbigg%281%2B%5Cfrac%7B12%7D%7B100%7D%5Cbigg%29%7D%5E5++-+1-+%5Cfrac%7B5+%5Ctimes+12%7D%7B100%7D+%5Cbigg%5D%5C%5C++%5C%5C++%3D45000++%5Cbig%5B%7B1.12%7D%5E5+-1+-++0.6+%5Cbig%5D%5C%5C++%5C%5C++%3D45000%5Cbig%5B1.76+-1.6+%5Cbig%5D+%5C%5C++%5C%5C++%3D+45000+%5Ctimes+0.16++%5C%5C++%5C%5C+%3D+7200 "= 45000\bigg[{\bigg(1+\frac{12}{100}\bigg)}^5 - 1- \frac{5 \times 12}{100} \bigg]\\ \\ =45000 \big[{1.12}^5 -1 - 0.6 \big]\\ \\ =45000\big[1.76 -1.6 \big] \\ \\ = 45000 \times 0.16 \\ \\ = 7200")
r = 12 %
t = 5 years
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