Question

Fabina borrows $Rs12,500$ at $12\%$ per annum for $3$ years at simple interest and Radhs bororows the same amount for the same time period at $10\%$ per annum compounded annually. Who pays more interest and by how much?

Answer 1

We have,

Principal value (p) = Rs 12,500

Time (t) = 3years.

Rate of interest (R) = 12% P.a.

now,

simple interest

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

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

$=Rs4500$ (for fabina)

Again,

Given that,

principal value $\left(p\right)=12,500$

$Time\left(t\right)=3years$

$Rate\left(R\right)=10$

now,

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

$=12,500(1+\frac{10}{100}{)}^3$

$=12,500(1+\frac{1}{10}{)}^3$

$=12,500\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}$

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

$=Rs16,637.50$ (For Radha)

C.I. for Radha

$=Amount-principalvalue.$

$=16,637.50-12,500$

$=4137.50$

Then, Fabina pays more interest

$=4,500-4137.50$

$=362.50Rs.$

Hence,

$Interest=Rs362.50$