Question

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is
A. 2 years
B. \[2\dfrac{1}{2}\] years
C. 3 years
D. 4 years

Answer 1

Hint: We had to only apply the compound interest formula that is \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\], where A is the amount after n years, P is the principal amount, r is the rate of interest and n is the number of years i.e. time period.

Complete step-by-step answer:
Let the time period be t years.
Now as we know that the compound interest is applied on Rs. 30,000.
So, the principal amount will be = P = Rs. 30,000
Now the amount after t years will be = A = Principal amount + Compound Interest for t years = 30,000 + 4347 = Rs. 34,347.
Now the given compounded rate of interest per annum is = r = 7%.
So, now let us apply compound interest formula.
\[ \Rightarrow 34,347 = 30,000{\left( {1 + \dfrac{7}{{100}}} \right)^t}\]
Dividing both sides of the above equation by 30000.
\[ \Rightarrow \dfrac{{34347}}{{30000}} = {\left( {1 + \dfrac{7}{{100}}} \right)^t}\]
\[ \Rightarrow \dfrac{{11449}}{{10000}} = {\left( {\dfrac{{107}}{{100}}} \right)^t}\]
\[ \Rightarrow {\left( {\dfrac{{107}}{{100}}} \right)^2} = {\left( {\dfrac{{107}}{{100}}} \right)^t}\]
So, comparing powers of both the sides of the above equation.
t = 2 years
So, the time period will be 2 years.
Hence, the correct option will be A.

Note: - Whenever we come up with this type of problem then there is only one method to find the value of any one of the elements (principal amount, final amount, rate of interest, time period). We had to apply compound interest formula and then put all the given values in that. And after solving that equation we will get the required value of that element (here time period in years). This will be the easiest and efficient way to find the solution of the problem.