Question

Ramesh invested Rs. 12,800 for 3 years at the rate of 10% p.a. compound interest. What is the total amount he will receive at the end of 3 years?

Answer 1

Hint: We have to find the total amount at the end of 3 years. So we have to compound the interest and add it to the principal amount for every year, for 3 years. We will use the formula for calculating the compound interest to get the answer. The formula for compound interest is as follows,
\[A = P{\left[ {1 + \dfrac{r}{n}} \right]^{nt}}\]
where $P$ is the initial principal amount, $r$ is the interest rate, $n$ is the number of compounding periods in a year, $t$ is the number of years and $A$ is the total amount at the end of $t$ years.

Complete step by step answer:
We will first collect the information given in the question. Ramesh invested Rs. 12,800 for 3 years. So, we have $P=12800$ and $t=3$. The rate is 10% p.a., so we have $r=0.10$ and we have to compound the interest per annum, that means every year, so we have $n=1$.
The formula to obtain the total amount by compound interest at the end of $t$ years is the following,
\[A = P{\left[ {1 + \dfrac{r}{n}} \right]^{nt}}\]
We have the given information and also the formula. Now, we will substitute the values that we have in the formula. We will get the following equation,
\[A=12800{{\left[ 1+\dfrac{0.10}{1} \right]}^{1\times 3}}\]
We will simplify this equation to calculate $A$ in the following manner:
\[\begin{align}
  & A=12800\times {{(1+0.1)}^{3}} \\
 & =12800\times {{(1.1)}^{3}} \\
 & =12800\times 1.331 \\
 & =17036.8
\end{align}\]

Therefore, the total amount that Ramesh will receive at the end of 3 years is Rs. 17036.8 .

Note:
In this question, we had to compound the interest once every year, hence $n=1$. It should be noted that if the question mentions compounding the interest in terms of months, $n$ has to be calculated carefully. There are multiple formulae to calculate simple and compound interests. The information given in the question should be carefully studied before choosing a suitable formula.