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Question

Answers

A). Rs. 916

B). Rs. 900

C). Rs. 961

D). Rs. 896

Answer

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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