Question

# If Pankaj deposits Rs 1,50,000 in a bank at 10 p.c.p.a for two years, what is the total amount he will get from the bank.

Hint:The concept of compound interest will be used here. We have been given the principal amount which is Rs 1,50,000, the rate of interest which is 10% and the time, which is 2 years. We will simply apply the formula to get the total amount received at the end of two years. The formula for calculating the total amount is-
$A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}$

We have been given that Pankaj deposits Rs 1,50,000 at the bank. This will be the initial principal amount. The rate of interest which is 10% is compounded annually for 2 years. This means that the interest at 10% is increased every year with respect to the total amount at the end of that year.
For example, if Rs 10 is compounded at 10% annually, the interest at the end of first year will be simply Re 1. But the interest in the second year will be applied on the total amount, that is Rs 11. So the amount at the end of second year will be Rs 12.1, and not Rs 12.
Now, we will use the formula for the total amount to find the amount received at the end of two years, which is given by-
$A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}$
Substituting P = 150000, r = 10 and t = 2 we get-
$A = 150000{\left( {1 + \dfrac{{10}}{{100}}} \right)^2}$
$A = 150000{\left( {\dfrac{{110}}{{100}}} \right)^2} = 150000{\left( {1.1} \right)^2}$
$A = 150000 \times 1.21 = Rs\;1,81,500$

This is the required final amount at the end of two years.

Note: A common mistake here is that students calculate the simple interest in this question, because they think that it is not mentioned which type of interest is being applied. But when we look at the question closely, we can see that the rate of interest is 10 p.c.p.a. Here, p.c.p.a stands for ‘percent compounded per annum’, which means that the interest is compounded annually.