Question
On what sum will the compound interest at $5\%$ per annum for $2$ years compounded annually be Rs. $164?$
✓
Answer
Let the sum be Rs. $x$.
We know that: $CI = A - P = \text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}-\text{P}$
$= \text{P}\Big[\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}-1\Big]$
$164= \text{x}\Big[\Big(1+\frac{5}{100}\Big)^{2}-1\Big]$
$164= \text{x}\Big[(1.05)^{2}-1\Big]$
$\text{x}=\frac{164}{0.1025}$
$=1,600$
Thus, the required sum is $Rs. 1,600.$
We know that: $CI = A - P = \text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}-\text{P}$
$= \text{P}\Big[\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}-1\Big]$
$164= \text{x}\Big[\Big(1+\frac{5}{100}\Big)^{2}-1\Big]$
$164= \text{x}\Big[(1.05)^{2}-1\Big]$
$\text{x}=\frac{164}{0.1025}$
$=1,600$
Thus, the required sum is $Rs. 1,600.$
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