Question & Answer
QUESTION

A man deposited Rs. 6000 in a bank at 5% simple interest. Another man deposited Rs. 5000 at 8% compound interest. After 2 years, the difference of their interest will be,
(a). Rs.230
(b). Rs.232
(c ). Rs.600
(d). Rs.832

ANSWER Verified Verified
- Hint: In the above question we will use the formula of compound interest and simple interest which is shown as below:
For compound interest we have, \[amount=p{{\left( 1+\dfrac{R}{100} \right)}^{n}}\] where p= principal, R = rate and n= time in years.

Complete step-by-step solution -

For simple interest we have, \[\text{interest}=\dfrac{P\times R\times T}{100}\] where p= principal, R= rate and T= time in years.

Given, for the first man: p= Rs.6000 , R = 5% , T= 2.
First man’s simple interest = $\dfrac{6000\times 5\times 2}{100}=Rs.600$
For the second man: p= Rs.5000 , R=8% , n= 2.
Second’s man compound interest = amount – principal.
  \[\begin{align}
  & =5000\left[ {{\left( 1+\dfrac{8}{100} \right)}^{2}}-1 \right] \\
 & =5000\left[ {{\left( \dfrac{27}{25} \right)}^{2}}-1 \right] \\
 & =5000\left[ \dfrac{729-625}{625} \right] \\
 & =\dfrac{5000\times 104}{625} \\
 & =Rs.832 \\
 & \therefore \text{ Difference in interest= }Rs.832-Rs.600=Rs.232 \\
\end{align}\]

Therefore, the correct option of the above question is option B.

Note: Just remember the formulae of compound interest and simple interest so that you can easily solve the above type of questions. Do not get confused with simple interest and compound interest. Simple interest is calculated on the principal, or original, amount of a loan. Compound interest is calculated on the principal amount and also on the accumulated interest.