Question

At what rate of compound interest per annum will a sum of \[Rs.1200\] become \[Rs.1348.32\] in 2 years?
(a) \[6%\]
(b) \[6.5%\]
(c) \[7%\]
(d) \[7.5%\]

Answer 1

Hint: Use the formula for calculating compound interest which is \[A=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\], where P is the initial amount on which interest is added, A is the amount to be paid by adding interest, T is the time for which interest is applied and R is the rate of interest.

Complete step-by-step answer:
We have to calculate the rate at which \[Rs.1200\] amounts to \[Rs.1348.32\] in 2 years.
We know that formula for calculating compound interest compounded annually, which is \[A=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\], where P is the initial amount on which interest is added, A is the amount to be paid by adding interest, T is the time for which interest is applied and R is the rate of interest.
We have \[P=Rs.1200,A=Rs.1348.32,T=2\].
We have to calculate the value of R.
Substituting the values in the above formula, we have \[1348.32=1200{{\left( 1+\dfrac{R}{100} \right)}^{2}}\].
Rearranging the terms, we have \[\dfrac{1348.32}{1200}={{\left( 1+\dfrac{R}{100} \right)}^{2}}\].
Thus, we have \[1.1236={{\left( 1+\dfrac{R}{100} \right)}^{2}}\].
Taking square root on both sides, we have \[1.06=1+\dfrac{R}{100}\].
Rearranging the terms, we have \[\dfrac{R}{100}=1.06-1=0.06\].
Thus, we have \[R=0.06\times 100=6%\].

Hence, the rate of interest at which \[Rs.1200\] amounts to \[Rs.1348.32\] in 2 years is \[6%\], which is option (a).

Note: Compound interest is the interest (extra money) that one needs to pay on a sum of money that has been taken as a loan. One must be careful of the fact that \[Rs.1348.32\] is the amount and not the interest. If we take this as interest, we will get an incorrect answer. To calculate the value of compound interest, we can subtract the principal from the amount.