Question

A person deposited a sum of money in a bank. The bank gives the interest at the rate of 8 % per annum compound interest compounded annually. After two year, the person got Rs 7290 as an amount from the bank. Find the sum of money the person has initially invested.

Answer 1

Hint: This is a simple question which is totally based on the basic formula of compound interest. The formula gives the amount generated by investing some money at a given rate of interest for a given duration of time. The formula is
$A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}\,\,\,\,\,\,\,\,\,\cdot \cdot \cdot \text{(i)}$
Here P is called principle – the sum of money invested or borrowed initially.
r is called the rate of compound interest per annum. This rate gives the amount by which principle increases in 1 year. That means in 1 year principle P increases to $P+\dfrac{r}{100}P$ .
t is called the time period during which the money has been invested or borrowed.
A is the amount which comes as a result of investment or borrow of the principle P for time period t.

Complete step-by-step answer:

In our question, let the person invest P sum of money. The rate of interest is given to be 8% per annum. So
$r=8%$
The duration for which the money has been invested is two years. So
$t=2\,\text{years}$
Amount the person has got after two years is Rs 7290. So
$A=\text{Rs }7290$
Using the equation (i) and putting the values of A, r and t, we can calculate P as:
$\begin{align}
  & 7290=P{{\left( 1+\dfrac{8}{100} \right)}^{2}} \\
 & \Rightarrow 7290=P{{\left( \dfrac{108}{100} \right)}^{2}}=P{{\left( \dfrac{27}{25} \right)}^{2}} \\
 & \Rightarrow P=7290\cdot \dfrac{{{25}^{2}}}{{{27}^{2}}} \\
 & \Rightarrow P=6250 \\
\end{align}$
So we get that the amount of money a person has invested is Rs 6250.

Note: If the rate of interest in the question is given in per quarter of a year then it should be converted to rate of interest per annum by multiplying it by 4. If we use the formula without converting the rate of interest then we will not get the correct result.