Question

Find the compound interest at the rate of $5\%$ for 3 years on that principal which in 3 years at the rate of $5\%$ per annum gives Rs. 12,000 as simple interest.

Answer 1

In first case,
S.I = Rs. 12000
Rate (R) $=5\%$ p.a
Period (T) = 3 years
$\therefore$ Principal $=\frac{S.I\times 100}{R\times T}=Rs.\frac{12000\times 100}{5\times 3}$
= Rs. 80000
In second case,
Principal (P) = Rs. 80000
Rate (R) $=5\%$ p.a
Period (n) = 3 years.
$\therefore$ Amount (A) $=P{(1+\frac{R}{100})}^n$
$=Rs.80000{(1+\frac{5}{100})}^3=Rs.80000{\left(\frac{21}{20}\right)}^3$
$=Rs.80000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20}=Rs.92610$
$\therefore$ C.I = A - P
= Rs. 92610 - 80000 = Rs. 12610