Question

Find the compound interest on Rs. 5000 for 3 years at 5% p.a. Find the simple interest also on Rs. 5000 for 3 years at 5% p.a. and calculate the difference in the interests.

Answer 1

Hint: We will first find the simple interest using the formula to calculate interest i.e. ${\displaystyle \frac{PRN}{100}}$ where, P is principal amount i.e. Rs. 5000, R is rate of interest i.e. 5% and N is time period i.e. 3 years. Then we will use the formula to find amount of compound interest i.e. $P{(1+{\displaystyle \frac{R}{100}})}^N$ where all the parameters remain the same. To calculate the compound interest formula to be used is $A=P+I$ where I am interested. From this, we will get compound interest. Then on taking the difference between simple and compound interest, we will get an answer.

Complete step-by-step answer:
Here, we will find simple interest (SI) using the formula ${\displaystyle \frac{PRN}{100}}$ where, P is principal amount i.e. Rs. 5000, R is rate of interest i.e. 5% and N is time period i.e. 3 years.
So, on substituting the values we get answer as
 $SI={\displaystyle \frac{PRN}{100}}$
 $SI={\displaystyle \frac{5000\times 5\times 3}{100}}$
On solving, we get as
 $SI=750$ …………………………….(1)
Now, we will calculate the amount for compound interest (CI) using the formula $P{(1+{\displaystyle \frac{R}{100}})}^N$ . On putting the values, we get as
 $A=5000{(1+{\displaystyle \frac{5}{100}})}^3$
On further solving, we get as
 $A=5000{(1+0.05)}^3$
 $A=5000{\left(1.05\right)}^3$
On simplification, we get as
 $A=5000(1.05\times 1.05\times 1.05)$
 $A=5788.125$
Now, to find compound interest, we will subtract principal amount from the amount i.e. $I=A-P=5788.125-5000=Rs.788.125$ .
So, CI is Rs. 788.125 ………………………(2)
Now, taking the difference between simple interest and compound interest, we get as $CI-SI=788.125-750=Rs.38.125$ .
Thus, the difference in interest is Rs. 38.125.

Note: Remember the amount is obtained by using the formula $P{(1+{\displaystyle \frac{R}{100}})}^N$ . Then to find compound interest we have to subtract the principal amount from the amount we got. Otherwise, the answer will be incorrect. Students generally make mistakes by considering the amount obtained as compound interest and thus the answer gets wrong. So, be clear with using the formula in order to avoid the mistake.