The difference between the compound interest and simple interest … - Vidyadip

Question

The difference between the compound interest and simple interest on a certain sum at 15% per annum for 3 years is Rs. 283.50. Find the sum.

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Answer

Given:
CI − SI = Rs. 283.50
R = 15%
n = 3 years
Let the sum be Rs. x.
We know that:
$\text{A}=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}$
$=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}$
$=\text{x}\Big(1+\frac{15}{100}\Big)^{3}$
$=\text{x}(1.15)^{3}\ ...(1)$
Also,
$\text{SI}=\frac{\text{PRT}}{100}=\frac{\text{x}(15)(3)}{100}=0.45\text{x}$
$\text{A}=\text{SI}+\text{P}=1.45\text{x}\ ...(2)$
Thus, we have:
$\text{x}(1.15)^{3}-1.45\text{x}=283.50$ [From (1) and (2)]
$1.523\text{x}-1.45\text{x}=283.50$
$0.070875\text{ x}=283.50$
$\text{x}=\frac{283.50}{0.070875}$
$=4,000$
Thus, the sum is Rs. 4,000.

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