Question

A sum of Rs. 15,000 is invested for 3 years at 13 % per annum compound interest. Calculate the compound interest.
(a) 6500.435
(b) 6689.245
(c) 6643.455
(d) 6276.585

Answer 1

Hint: The formula to calculate compound interest for principal amount P at the rate of R % for n years is given by \[I = P{\left( {1 + \dfrac{R}{{100}}} \right)^n} - P\]. Substitute the values in this formula to calculate the compound interest.

Complete step-by-step answer:
Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan.
Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compounded years minus the principal amount.
The formula to calculate the compound interest is given as follows:
\[I = P{\left( {1 + \dfrac{R}{{100}}} \right)^n} - P..........(1)\]
The value of the principal amount P is Rs. 15,000. The rate at which it is compounded annually is 13 % and the duration is for 3 years. Using the formula in equation (1), we have:
\[I = 15,000{\left( {1 + \dfrac{{13}}{{100}}} \right)^3} - 15,000\]
Simplifying the term inside the bracket, we have:
\[I = 15,000{\left( {1 + 0.13} \right)^3} - 15,000\]
\[I = 15,000{\left( {1.13} \right)^3} - 15,000\]
The value of the cube of 1.13 is 1.442897. Substituting the value, we have:
 \[I = 15,000\left( {1.442897} \right) - 15,000\]
We know that 15,000 multiplied with 1.442897 is 21,643.455‬, then, we have:
\[I = 21,643.455 - 15,000\]
The compound interest calculate is as follows:
\[I = 6,643.455\]
Hence, the correct answer is option (c).

Note: The value of the amount after n years is given by \[P{\left( {1 + \dfrac{R}{{100}}} \right)^n}\]. To get the value of the compound interest, you need to subtract it with the principal amount.