Question

Ambadas took a loan of Rs 96,000 at compound interest from a bank to drill a well in his field. If the rate is 6.25 p.c.p.a., what amount will he have to pay to the bank if he returns the loan after 2 years? How much money would he have saved had he been able to borrow the same amount at simple interest for the same period at the same rate?

Answer 1

Principal = Rs 96,000
Rate of interest = 6.25% p.a.
Number of years (N) = 2 years
In case of compound interest, amount$=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =96000{\left(1+\frac{6.25}{100}\right)}^2 \\ =96000{\left(1+\frac{625}{10000}\right)}^2 \\ =96000{\left(1+\frac{1}{16}\right)}^2 \\ =96000{\left(\frac{17}{16}\right)}^2 \\ =96000\times \frac{17}{16}\times \frac{17}{16} \\ =\mathrm{Rs}108375 \end{gathered}$$

The amount is Rs 108375.
Compound Interest = Amount − Principal = 108375 − 96,000 = Rs 12375
∴ Compound Interest = Rs 12375
Simple Interest$=\frac{\mathrm{Principal}\times \mathrm{Rate}\times \mathrm{Time}}{100}=\frac{96000\times 6.25\times 2}{100}=\mathrm{Rs}12000$
Difference between Compound Interest and Simple Interest= Compound Interest − Simple Interest
= Rs 12375 − Rs 12000 = Rs 375
So, he would have saved Rs 375 if he had borrowed the same amount at simple interest for the same period at the same rate.