Question

On what sum will the compound interest at $5\%$ p.a. annum for 2 years compounded annually be Rs. 164?

Answer 1

Let Principal (P) = Rs. 100
Rate (R) $=5\%$ p.a.
Period (n) = 2 years
$\therefore$ C.I $=P[{(1+\frac{R}{100})}^n-1]$
$=Rs.100[{(1+\frac{5}{100})}^2-1]$
$=Rs.100[{\left(\frac{21}{20}\right)}^2-1]=Rs.100[\frac{441}{400}-1]$
$=Rs.100\times \frac{441-400}{400}=Rs.100\times \frac{41}{400}$
$=Rs.\frac{41}{4}$
If C.I is $Rs.\frac{41}{4}$, then principal = Rs. 100
If C.I is Re. 1, then principal $=Rs.\frac{100\times 4}{41}$
If the C.I is Rs. 164 the principal
$=Rs.\frac{100\times 4\times 164}{41}=Rs.1600$