Question

A sum of money invested at compound interest amounts to Rs. 800 in 3 years and to Rs. 840 in 4 years. The rate of interest per annum is-
A. 3%
B. 4%
C. 5%
D. 6%

Answer 1

Hint: We will simply use the formula of compound interest i.e. $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$, where A stands for the value of amount, P stands for the principal amount, r stands for the rate and n stands for the number of years or number of intervals and we will find the rate of interest per annum as asked by the question.

Complete step-by-step answer:
Let the rate of interest per annum be r.
As we know the formula for compound interest is $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$. The compound interest for the first 3 years is given as 800. Rate will be r and principal amount will be P. We will put these values in the formula for compound interest we will have-
$\to 800$ = $P{\left( {1 + \dfrac{r}{{100}}} \right)^3}$
We will take this equation as equation 1, we get-
$\to 800 = P{\left( {1 + \dfrac{r}{{100}}} \right)^3}$ (equation 1)
Now, the value of compound interest for four years is given as 840. Rate will be r and principal amount P. We will put these values in the formula for compound interest we will have-
$\to 840 = P{\left( {1 + \dfrac{r}{{100}}} \right)^4}$
We will take the above equation as equation 2, we will have-
$\to 840 = P{\left( {1 + \dfrac{r}{{100}}} \right)^4}$ (equation 2)
Now, we will divide equation 1 by equation 2 in order to solve this further. After doing so we will have-
$
   \to \dfrac{{800}}{{840}} = \dfrac{{P{{\left( {1 + \dfrac{r}{{100}}} \right)}^3}}}{{P{{\left( {1 + \dfrac{r}{{100}}} \right)}^4}}} \\
    \\
   \to \dfrac{{80}}{{84}} = \dfrac{1}{{\left( {1 + \dfrac{r}{{100}}} \right)}} \\
    \\
   \to \dfrac{{20}}{{21}} = \dfrac{1}{{\left( {1 + \dfrac{r}{{100}}} \right)}} \\
$
By cross multiplication, we will have-
$
   \to 20\left( {1 + \dfrac{r}{{100}}} \right) = 21 \\
    \\
   \to 20 + \dfrac{{20r}}{{100}} = 21 \\
    \\
   \to \dfrac{r}{5} = 1 \\
    \\
   \Rightarrow r = 5\% \\
$
Thus, the rate of interest per annum is 5%.

Note: In such questions, let consider rate be r and apply the formula for compound interest i.e. $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$. The formula should be memorised in an exact manner and the values should be put correctly in order to get the correct answer.