Question

What will be the compound interest on a sum of $Rs25000$ after three years at the rate of $12$ percent per annum?
A) $Rs\,10123.20$
B) $Rs\,11123.20$
C) $Rs\,12123.20$
D) $Rs\,13123.20$

Answer 1

Hint: The problem can be solved easily with the concept of compound interest. Compound interest is the interest calculated on the principal and the interest of the previous period. The amount in compound interest to be cumulated depends on the initial principal amount, rate of interest and number of time periods elapsed. The amount A after a certain number of time periods T on a given principal amount P at a specified rate R compounded annually is calculated by the formula: $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$ .

Complete step-by-step answer:
In the given problem,
Principal $ = P = Rs\,25000$
Rate of interest $ = 12\% $
Time Duration $ = 3\,years$
In the question, the period after which the compound interest is compounded or evaluated is not given. So, we assume that the compound interest is compounded annually by default.
So, Number of time periods$ = n = 3$
Now, The amount A to be paid after a certain number of time periods n on a given principal amount P at a specified rate R compounded annually is calculated by the formula: $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$ .
Hence, Amount $ = A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$
Now, substituting all the values that we have with us in the formula $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$, we get,
$ \Rightarrow A = Rs\,25000{\left( {1 + \dfrac{{12}}{{100}}} \right)^3}$
Taking LCM, we get,
Cancelling common factors in numerator and denominator, we get,
$ \Rightarrow A = Rs\,25000{\left( {\dfrac{{112}}{{100}}} \right)^3}$
$ \Rightarrow A = Rs\,25000{\left( {\dfrac{{28}}{{25}}} \right)^3}$
Expanding the cubic expression,
$ \Rightarrow A = Rs\,25000 \times \left( {\dfrac{{28}}{{25}}} \right) \times \left( {\dfrac{{28}}{{25}}} \right) \times \left( {\dfrac{{28}}{{25}}} \right)$
Cancelling common factors in numerator and denominator, we get,
$ \Rightarrow A = Rs\,8 \times 28 \times 28 \times \left( {\dfrac{{28}}{5}} \right)$
Simplifying the calculations, we get,
$ \Rightarrow A = Rs\,35123.2$
Amount that we receive after $3$ years $ = $Principal$ + $Compound interest
Substituting the values of principal and amount that we calculated using the formula in the equation, we get,
$ \Rightarrow \,Rs\,35123.2 = Rs\,25,000\, + C.I.$
Shifting the terms in the equation to find the compound interest. So, we get,
$ \Rightarrow C.I. = \,Rs\,35123.2 - Rs\,25,000\,$
Simplifying the calculations, we get,
$ \Rightarrow C.I. = \,Rs\,10123.2$
Therefore, the compound interest on the sum of $Rs25000$ after three years at the rate of $12$ percent per annum is $Rs\,10123.2$.

Note: Time duration is not always equal to the number of time periods. The equality holds only when the compound interest is compounded annually. If the compound interest is compounded half yearly, then the number of time periods doubles in the given time duration and the rate of interest in each time period becomes half of the specified rate of interest.