Question
Answers

The compound interest on Rs 4000 at 10% per annum for 2 years 3 months compounded annually is
A). Rs. 916
B). Rs. 900
C). Rs. 961
D). Rs. 896

Answer
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Hint: First we’ll find the compound interest for 2 years by using its formula. Rest of the 2 months’ interest will be simple because it’s given that the compound interest will be applied annually. In the end, we’ll add both the interest and subtract from the principal amount.

Complete step by step solution:
Here, we have given the principal amount (P) as 4000 and interest (r) 10% annually. As we’ll divide the total time duration into two parts because in the time span of 2 years compound interest will be applied and for the rest of the 3 months simple interest will be applied.
The formula for the compound interest is $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$
Where A is the total amount, P is the principal amount, r is the rate of interest and n is the time duration.
According to our question, $P=4000, r=10\%, n =2 $years. On Calculation A we get,
\[ A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n} \\
   \Rightarrow A = 4000{\left( {1 + \dfrac{{10}}{{100}}} \right)^2} \\
   \Rightarrow A = P{\left( {1 + \dfrac{1}{{10}}} \right)^2} \\
   \Rightarrow A = 4000{\left( {\dfrac{{11}}{{10}}} \right)^2} \\
   \Rightarrow A = 4000 \times \dfrac{{121}}{{100}} \\
   \Rightarrow A = 4840{\text{ Rs}}{\text{.}} \]
Hence the amount after 2 years will be 4840 and it’ll only work as the principal amount for simple interest. The formula for the simple interest is = $\dfrac{{PRT}}{{100}}$, where P is the principal amount, R is the rate of interest, and T is time spam.
On putting the values, we get,
$ \dfrac{{PRT}}{{100}} \\
   = \dfrac{{4840 \times 10 \times 1}}{{100 \times \times 4}} \\
   = \dfrac{{4840 \times 1 \times 1}}{{10 \times \times 4}} \\
   = \dfrac{{484 \times 1 \times 1}}{{1 \times \times 4}} \\
   = 121 $
So, the total amount after 2 years and 3 months will be Rs 4840 + Rs 121 which is equal to Rs 4961.
Total interest will be = total amount after 2 years 3 months- principal amount
That is, $Rs 4961 – Rs 4000$
And, Rs. 961

Hence, option (c) is the correct option.

Note: Students usually make mistakes in such a type of problem where for some time period compound interest is applied and for some time period, simple interest is applied. It’s always recommended from our side to read the question carefully, especially the interest section. Whether the interest is applied monthly or annually also of which kind, simple of the compound.