# Calculate the amount and the compound interest on $Rs.12,500$ in $3$ years when the rates of interest for successive years are $8\%$ , $10\%$ and $10\%$ respectively.

$\text{A)Rs16,335 and Rs 3,835}$

$\text{B)Rs14,853 and Rs 2,353}$

$\text{C)Rs15,664 and Rs 3,164}$

$\text{A)Rs 15,664 and Rs 3,164}$

Answer

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**Hint:**To solve the question we need to know the concept of compound interest. So the formula used to find compound interest is the difference of the Amount and principal. The formula for finding the amount is $A=P\left( 1+\dfrac{{{R}_{1}}}{100} \right)\left( 1+\dfrac{{{R}_{2}}}{100} \right)\left( 1+\dfrac{{{R}_{3}}}{100} \right)$. On substituting the value in the formula we will get the amount and the compound interest.

**Complete step by step answer:**

The question asks us to find the amount and the compound interest on $Rs.12,500$ in $3$ years when the rates of interest for successive years are $8\%$ , $10\%$ and $10\%$ respectively. The rate given in the question is successive for the three years. First attempt will be to find the Amount after $3$years. The formula used will be:

$\Rightarrow A=P\left( 1+\dfrac{{{R}_{1}}}{100} \right)\left( 1+\dfrac{{{R}_{2}}}{100} \right)\left( 1+\dfrac{{{R}_{3}}}{100} \right)$

In the above formula P is the principal, A is the amount which we will get after the time period, T os the time and R is the rate at which,

On substituting the values on the formula we get:

$\Rightarrow A=12,500\left( 1+\dfrac{8}{100} \right)\left( 1+\dfrac{10}{100} \right)\left( 1+\dfrac{10}{100} \right)$

We will be using the BODMAS rule to calculate the above expression according to which the expression inside the bracket is calculated first and then multiplication is done. So on calculating like this we get:

$\Rightarrow A=12,500\left( 1+0.08 \right)\left( 1+0.1 \right)\left( 1+0.1 \right)$

$\Rightarrow A=12,500\left( 1.08 \right)\left( 1.1 \right)\left( 1.1 \right)$

The next step in the calculation is to multiply the numbers to find the amount.

\[\Rightarrow A=16,335\]

So the amount at the end of the time period is \[Rs16,335\].

The next step will be to find the Compound Interest of the principal. The formula used to find it is:

$\Rightarrow \text{C}\text{.I}\text{. = Amount - principal}$

On substituting the value in the formula we get:

$\Rightarrow \text{C}\text{.I}\text{. = 16335 - 12500}$

$\Rightarrow \text{C}\text{.I}\text{. = Rs 3835}$

$\therefore $ The amount and the compound interest on $Rs.12,500$ in $3$ years when the rates of interest for successive years are $8\%$ , $10\%$ and $10\%$ respectively is $\text{A)Rs16,335 and Rs 3,835}$.

**So, the correct answer is “Option A”.**

**Note:**You need to remember the formula to find the amount when the principal rupees is compounded annually. The formula is $A=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}$. While in case of the rates are when done successively the formula becomes $A=P\left( 1+\dfrac{{{R}_{1}}}{100} \right)\left( 1+\dfrac{{{R}_{2}}}{100} \right)\left( 1+\dfrac{{{R}_{3}}}{100} \right)$. There is a possibility that students apply each given rate to the principal amount and then find the final amount. This will lead to a grave mistake as they will be using year as 3 for each calculation.

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