Question

Find the compound interest on ₹.\[3000\]for two years at \[8\% \] per annum compounded quarterly.
A. $524.98$
B. $534.98$
C. $544.98$
D. $514.98$

Answer 1

Hint: Using value of principal sum, rate of interest and time in the formula of compound interest to get interest on the given amount in the formula.
\[C.I = \left[ {P{{\left( {1 + \dfrac{R}{{100}}} \right)}^T} - 1} \right]\]

Complete step by step answer:
Where P is the principal sum,
R is the rate per annum,
T is the period of time given,
(1) Given \[P = 3000\] , \[R = 8\% \] (p.a), \[T = 2\] years
But it is given that compound interest is calculated quarterly.
\[\therefore \] We will firstly change time and rate quarterly.
(2) For quarterly, rate gets divided by four times and time is multiplied by $4$.
\[ \Rightarrow \,\,Time\, = 2\,years\]
In quarters \[ = 2 \times 4 = 8\]
\[Rate = 8\% \,\,(p.a.)\]
In quarters \[ = \dfrac{8}{4} = 2\% \]
(3) Using the value of \[T = 8\] and \[R\, = 2\% \] in compound interest formula.
\[C.I = P\left[ {{{\left( {1 + \dfrac{R}{{100}}} \right)}^T} - 1} \right]\]
\[ \Rightarrow C.I = 3000\left[ {{{\left( {1 + \dfrac{2}{{100}}} \right)}^8} - 1} \right]\]
\[ = 3000\left[ {{{\left( {1 + \dfrac{1}{{50}}} \right)}^8} - 1} \right]\]
\[ = 3000\left[ {{{\left( {\dfrac{{51}}{{50}}} \right)}^8} - 1} \right]\]
\[ = 3000\left[ {{{(1.02)}^8} - 1} \right]\]
\[ = 3000\,[1.171 - 1]\]
\[ = 3000\,\,(0.171659)\]
\[C.I = \]₹.\[514.98\,\,(approx.)\]

Hence, the correct option is D.

Additional Information: Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.

Note: While using the formula of compound interest, students should be careful in putting the values of rate of interest and time, these should be accurate otherwise they will not get the suitable answer.