Question

Fabina borrows ₹12,500 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 and by how much?

• A. Fabina pays ₹362.50 more than Radha.
• B. Radha pays ₹482.50 more than Fabina.
• C. Radha pays ₹362.50 more than Fabina.
• D. Fabina pays ₹482.50 more than Radha.

Answer 1

The correct option is A

Fabina pays ₹362.50 more than Radha.

Here, Principal (P) = ₹12,500, Time (T) = 3 years, Rate of interest (R) = 12% p.a

We know that S.I. = $\frac{PRT}{100}$

where, S.I. is the simple interest, P is the principal, R is the rate of interest per annum and T is the time(number of years).

Simple Interest for Fabina = $\frac{P\times R\times T}{100}$ = $\frac{12500\times 12\times 3}{100}$ = ₹4500.

We know that C.I. = $P[1+\frac{R}{100}{]}^n$

where, C.I. is the compound interest, P is the principal, R is the rate of interest per annum and n is the time(number of years).

Amount(A) paid by Radha at the end of 3 years,

A = $1500{(1+\frac{10}{100})}^3$

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

=$12500{\left(\frac{11}{10}\right)}^3$
=$12500\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}$
= ₹16,637.50
$\therefore$ C.I. for Radha = A - P = ₹16,637.50 - ₹12,500 = ₹4,137.50
Hence, Fabina pays ₹362.50 (= ₹4,500 - ₹4,137.50) more interest than Radha.