Question
Find the difference between the simple interest and the compound interest on $Rs. 5000$ for $2$ years at $9\%$ per annum.
✓
Answer
Principal $(p) = Rs. 5000$
Rate $(R) = 9\%$ p.a.
Time $(n) = 2$ years
$\therefore\text{S.I.}=\frac{\text{PRT}}{100}$
$=\frac{5000\times9\times2}{100}$
$=\text{Rs.}\ 900$
New amount at $C.I. =\text{P}\Big(1+\frac{\text{R}}{100}\Big)^\text{n}$
$=\text{Rs.}\ 5000\Big(1+\frac{9}{100}\Big)^\text{2}$
$=\text{Rs.}\ 5000\times\frac{109}{100}\times\frac{109}{100}$
$=\text{Rs.}\ \frac{11881}{2}$
$=\text{Rs.}\ 5940.50$
$\therefore C.I = A - P = Rs. 5940.50 - Rs. 5000 = Rs. 940.50$
$\therefore$ Difference between $C.I.$ and $S.I. = Rs. 940.50 - Rs. 900 = Rs. 40.50$
Rate $(R) = 9\%$ p.a.
Time $(n) = 2$ years
$\therefore\text{S.I.}=\frac{\text{PRT}}{100}$
$=\frac{5000\times9\times2}{100}$
$=\text{Rs.}\ 900$
New amount at $C.I. =\text{P}\Big(1+\frac{\text{R}}{100}\Big)^\text{n}$
$=\text{Rs.}\ 5000\Big(1+\frac{9}{100}\Big)^\text{2}$
$=\text{Rs.}\ 5000\times\frac{109}{100}\times\frac{109}{100}$
$=\text{Rs.}\ \frac{11881}{2}$
$=\text{Rs.}\ 5940.50$
$\therefore C.I = A - P = Rs. 5940.50 - Rs. 5000 = Rs. 940.50$
$\therefore$ Difference between $C.I.$ and $S.I. = Rs. 940.50 - Rs. 900 = Rs. 40.50$
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