Question

Find the compound interest on Rs.7500 at 4% per annum for 2 years, compounded annually
\[
  (a){\text{ Rs}}{\text{. 612}} \\
  (b){\text{ Rs}}{\text{. 412}} \\
  (c){\text{ Rs}}{\text{. 782}} \\
  (d){\text{ Rs}}{\text{. 112}} \\
\]

Answer 1

Hint – In this problem use the direct formula for compound interest that is $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}$where r is the rate that is 4%. Take the principal amount as Rs. 7500. This will help getting the value of A directly, then the compound interest will simply be the subtraction of A and the principal value.

Complete step-by-step answer:
As we know the formula for compound interest which is given as
$ \Rightarrow A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}$…………………………. (1)
Where A = total amount received after the compound interest.
             P = Principle amount.
             r = rate of interest.
             t = time in years.
Therefore compound interest (C.I) = A - P
Now it is given that P = Rs. 7500, r = 4%, t= 2 years
Therefore, C.I = $P{\left( {1 + \dfrac{r}{{100}}} \right)^t} - P$
Now substitute the value we have,
Therefore, C.I = $7500{\left( {1 + \dfrac{4}{{100}}} \right)^2} - 7500$
$ \Rightarrow C.I = 7500{\left( {1 + \dfrac{1}{{25}}} \right)^2} - 7500$
$ \Rightarrow C.I = 7500{\left( {\dfrac{{26}}{{25}}} \right)^2} - 7500$
$ \Rightarrow C.I = 7500\left( {\dfrac{{26}}{{25}}} \right)\left( {\dfrac{{26}}{{25}}} \right) - 7500$
$ \Rightarrow C.I = 12\left( {26} \right)\left( {26} \right) - 7500$
$ \Rightarrow C.I = 8112 - 7500 = 612$
So the compound interest is Rs. 612
Hence option (A) is correct.

Note – There is always a confusion regarding the basics of simple interest and compound interest. Simple interest is calculated on the principal or original amount of a loan whereas compound interest is calculated on the principal amount and also on the accumulated interest of previous periods and thus it can also be termed as interest of interests.