Question

A sum of money invested at compound interest amounts in 3 years to Rs.2400 and in 4 years to Rs.2520. Find the interest rate per annum.
A. 5%
B. 6%
C. 10%
D. 12%

Answer 1

Hint: For solving this equation, one should have prior knowledge about the concept of compound interest and also remember to use the formula of compound interest i.e. $A = P{\left( {1 + \dfrac{r}{n}} \right)^{nt}}$, use this information to approach the solution of the question.

Complete step-by-step answer:
According to the given information we know that money invested amounts in 3 years is Rs. 2400 and the money invested in 4 years is Rs. 2520
Let Rs. x be the sum of money invested and r% is the interest rate per annum
Since we know that the formula of compound interest is given by $A = P{\left( {1 + \dfrac{r}{n}} \right)^{nt}}$here A is the final amount, P initial principal balance, r = interest rate, n is the number of times interest applied per time period and t is the number of time periods elapsed
Now substituting the values in the above formula
For case I:
$2400 = x{\left( {1 + \dfrac{r}{{100}}} \right)^3}$ taking this equation as equation 1
Now for case II:
$2520 = x{\left( {1 + \dfrac{r}{{100}}} \right)^4}$ taking this equation as equation 2
Now applying the division operation between equation 2 and equation 1 we get
\[\dfrac{{2520}}{{2400}} = \dfrac{{x{{\left( {1 + \dfrac{r}{{100}}} \right)}^4}}}{{x{{\left( {1 + \dfrac{r}{{100}}} \right)}^3}}}\]
$ \Rightarrow $\[\dfrac{{2520}}{{2400}} = \left( {1 + \dfrac{r}{{100}}} \right)\]
$ \Rightarrow $\[\dfrac{r}{{100}} = \dfrac{{2520}}{{2400}} - 1\]
$ \Rightarrow $\[\dfrac{r}{{100}} = \dfrac{{2520 - 2400}}{{2400}}\]
$ \Rightarrow $\[r = \dfrac{{120}}{{24}}\]
$ \Rightarrow $\[r = 5\% \]
Therefore, rate per annum is 5%

So, the correct answer is “Option A”.

Note: Remember the formulas of simple interest and be aware of the terms such as principal amount, rate. This question can also be solved by using the formula of simple interest as for a particular year taken into consideration compound interest can be considered as simple interest as compound interest is simple interest where principal gets updated every year then we will use the formula of interest rate and for that first we will calculate simple interest from given values.