Question

At what rate will Rs.2000 amount to Rs.2315.25 in 3 years at compound interest?

Answer 1

Hint- In this question we should know at first we should take a look at the given values and then we should apply the formula of compound interest i.e $A = P{\left( {1 + r} \right)^t}$ which will help to solve the question, but before we also mention the values to be substituted to find the rate.

Complete step-by-step answer:
So it is given to us that Rs. 2000 amounts to 2315.25 in 3 years at compound interest.
Now we have to find out what percent will it be.
Using compound interest formula,
$A = P{\left( {1 + r} \right)^t}$
Where A is the amount A= 2315.25
P is the principle P= 2000
r is the rate r=?
t is the time t= 3 years
Substitute the values,
$\Rightarrow A = P{\left( {1 + r} \right)^t} \\\ \Rightarrow 2315.25 = \left( {2000} \right){\left( {1 + r} \right)^3} \\\ \Rightarrow {\left( {1 + r} \right)^3} = 1.1576 \\\ \Rightarrow 1 + r = 1.05 \\\ \Rightarrow r = 0.05 \\\ \Rightarrow r = 5\% \\\$
Therefore, Rate = 5%.

Note- In this question one should know that generally there is also n (number of time interest applied per time period) in the formula of compound interest which we didn’t use as it was not given and not required. Then be aware while putting the values as it can lead to mistakes.