# Find the compounded interest of Rs.24000 at 15% per annum for $2\dfrac{1}{3}$years.${\text{A}}{\text{. Rs}}{\text{. 8000}} \\ {\text{B}}{\text{. Rs}}{\text{. 9237}} \\ {\text{C}}{\text{. Rs}}{\text{. 9327}} \\ {\text{D}}{\text{. Rs}}{\text{. 9732}} \\$
Hint: Compound interest is the sum of the principle and the interest where principle is the amount of loan or the deposit on which interest is calculated at a rate for a time period. Compound interest is generally found by $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$where P is the principle on which interest is to be calculated for a given rate $r$. The compound can also be calculated half-yearly, quarterly, and monthly. In the question, the time has been given as $2\dfrac{1}{3}$ year which is equal to 2 years and 4 months.
Complete step by step solution:Substitute the values for principal, rate of interest and time in the formula $CI = P{\left[ {1 + \dfrac{r}{{100}}} \right]^t} - P$ to determine the value of the compound interest.
$CI = P{\left[ {1 + \dfrac{r}{{100}}} \right]^t} - P \\ = 24000{\left[ {1 + \dfrac{{15}}{{100}}} \right]^{\dfrac{7}{3}}} - 24000 \\ = 24000\left( {{{\left( {1.15} \right)}^{\dfrac{7}{3}}} - 1} \right) \\ = 24000\left( {1.385 - 1} \right) \\ = 24000(0.385) \\ = 9240 \\$
Here, while calculating we have considered for the approximation so, the nearest value of 9240 matching with the option is 9237. Hence, the compound interest on Rs.24000 at 15% per annum for $2\dfrac{1}{3}$ years is 9237.
Note: If the interest rates are different for every year, compound interest can also be calculated by $A = P\left( {1 + \dfrac{{{r_1}}}{{100}}} \right)\left( {1 + \dfrac{{{r_2}}}{{100}}} \right).......$ for shortcut methods, but interest is being calculated year by year for better understanding. This type of question can be solved by two methods. Alternatively, the interest can be calculated by using the formula of simple interest foe every year and then, adding all of them. The amount calculated on the first year will act like the principal amount for the second year and so on.