Question

Calculate the compound interest on the principal amount of Rs. 10800 for 3 years at a rate of interest of $12\dfrac{1}{2}$% per annum compounded annually.

Answer 1

Hint: First, use the formula: $A=P{{\left( 1+\dfrac{R}{100} \right)}^{t}}$ for calculating the amount for compound interest. Put the value given in this question to get the value for A. Then, use the formula: Compound Interest (CI) = Amount (A) – Principal (P) for calculating the compound interest which is the final answer.

Complete step-by-step answer:
In this question, we need to find to calculate the compound interest on the principal amount of Rs. 10800 for 3 years at a rate of $12\dfrac{1}{2}$% per annum compounded annually.

We are given that:

Principal amount, P = Rs. 10800

Rate of interest, R = $12\dfrac{1}{2}=\dfrac{25}{2}$% per annum

Time, t = 3 years

We will now calculate the principal amount of Rs. 10800 after 3 years at a rate of $\dfrac{25}{2}$% per annum compounded annually.

We know that the formula for amount for compound interest is the following:

$A=P{{\left( 1+\dfrac{R}{100} \right)}^{t}}$, where A is the amount after t time.

Now, we will substitute P = Rs. 10800, R = $\dfrac{25}{2}$% per annum, and t = 3 years in the above formula.

Substituting these values in the above formula, we will get the following:

$A=10800{{\left( 1+\dfrac{25}{200} \right)}^{3}}$

$A=10800{{\left( 1+\dfrac{1}{8} \right)}^{3}}$

$A=10800{{\left( \dfrac{9}{8} \right)}^{3}}$

$A=10800\times \dfrac{9}{8}\times \dfrac{9}{8}\times \dfrac{9}{8}=15377.34$

So, the amount on the principal amount of Rs. 10800 after 3 years is Rs. 15377.34

Now, we know that Compound Interest (CI) = Amount (A) – Principal (P)

So, using the above formula, we will get the following:

Compound Interest (CI) = Rs. 15377.34 – Rs. 10800 = Rs. 4577.34

Hence, the compound interest on the principal amount of Rs. 10800 for 3 years at a rate of

interest of $12\dfrac{1}{2}$% per annum compounded annually is Rs. 4577.34

Note: In this question, it is very important to know about compound interest and the formula to calculate amount and subsequently the compound interest. Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.