Question

Maria borrowed $Rs.12500$ at $12\%$ per annum for $3$ years at simple interest and Radha borrows the same amount for the same time period at $10\%$ per annum compounded annually .Who pays more interest by how much ?

Answer 1

Given:

Principal (P) $=Rs.12,500$

Time (T) $=3$ years,

Rate of interest (R) $=12\%$ p.a.

Simple Interest for Maria $=\frac{(P\times R\times T)}{100}$

$=\frac{(12500\times 12\times 3)}{100}$

$=125\times 36$

$=Rs.4,500$

Amount for Radha,

Given:

$P=Rs.12,500,R=10\%,n=3$ years

Amount $\left(A\right)=P(1+\frac{R}{100}{)}^n$

$=12500(1+\frac{10}{100}{)}^3$

$=12500(1+\frac{1}{10}{)}^3$

$=12500\times (\frac{11}{10}{)}^3$

$=\frac{(12500\times 11\times 11\times 11)}{1000}$

$=\frac{125\times 1331}{10}=\frac{166375}{10}$

$=Rs.16,637.50$

C.I. for Radha = A $–$ P

$=Rs.16,637.50–Rs.12,500=Rs.4,137.50$

Hence, Maria pays more interest

$=Rs.4,500–Rs.4,137.50=Rs.362.50$