Question

What amount of money should Mohan in a bank in order to get Rs.1323 in 2 years at 5% compounded annually?

Answer 1

Hint: Use the formula to calculate the amount in compound interest. Substitute the values given as per the question and find the principal.

Complete step-by-step answer:
We have been given the amount = Rs.1323

The rate of interest = 5%

Time period = 2 years

We need to find the principal, P.

The interest rate is the amount charged on top of the principal by a lender to a borrower for the use of assets.

 It is said that the amount is compounded annually. Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods.

Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one.

Amount \[=P{{\left[ 1+\dfrac{R}{100} \right]}^{n}}\].

We need to find P.

\[\begin{align}

  & 1323=P{{\left[ 1+\dfrac{5}{100} \right]}^{2}} \\

 & 1323=P{{\left[ 1+\dfrac{1}{20} \right]}^{2}} \\

 & 1323=P{{\left[ 1+0.05 \right]}^{2}} \\

 & 1323=P{{\left( 1.05 \right)}^{2}} \\

\end{align}\]

\[\therefore P=\dfrac{1323}{1.05\times 1.05}=1200\]

Thus we got the principal as, P = Rs.1200.

Note: Simple Interest and compound interest are different. 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 of previous periods and can be regarded as “interest on interest”.