Question

Fabina borrows $₹12,500$ at $12\text{\%}$ per annum for $3$ years at simple interest and Radha borrows the same amount for the same time period at $10\text{\%}$ per annum, compounded annually. Who pays more interest and by how much?

• A. $₹632.5$
• B. $₹326.5$
• C. $₹362.5$
• D. $₹4500$

Answer 1

The correct option is C $₹362.5$

In case of Fabina:

$P=₹12,500$

$R=12\text{\% per annum}$

$T=3years$

$S.I.=\frac{P\times R\times T}{100}$

$=\frac{12500\times 12\times 3}{100}=₹4500$

In case of Radha:

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

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

$=12500\times \frac{110}{100}\times \frac{110}{100}\times \frac{110}{100}$

$=₹16637.50$

Compound interest = Amount ($A$) - Principal ($P$)

$=₹16637.50-₹12500$

$=₹4137.50$

Clearly, Fabina pays more than Radha.

$\text{Difference}=₹4500-₹4137.50=₹362.5$