Question

Find the time, in years in which Rs. 4000 produce Rs. 630.50 as compound interest 5 per cent p.a. interest being compounded annually.

Answer 1

Hint: Formula of compound interest is $CI = P\left\{ {{{\left[ {1 + \dfrac{R}{{100}}} \right]}^N} - 1} \right\}$, here P is the principle amount, CI is the compound interest, R is the rate of interest and N is the time in years, use this to solve the question and find the value of time period, N.

Complete step-by-step answer:
We have been given in the question the values of Principal amount, compound interest and the rate of interest. And we have to find the time, in years in which the given principal amount produces the interest of Rs.630.50 at a given rate of interest.
So, the values are -
Principle amount, $P = Rs.4000$
Compound Interest, $CI = Rs.630.50$
Rate of interest, $R = 5\% $
To find: N, the time, in years in which Rs.4000 produces Rs. 630.50 as compound interest at a rate of 5%.
So, using the formula of compound interest $CI = P\left\{ {{{\left[ {1 + \dfrac{R}{{100}}} \right]}^N} - 1} \right\}$,
Here, P is the principle amount, CI is the compound interest, R is the rate of interest and N is the time period.
 Substituting the values of P, CI, R in the given formula, we get,
$630.50 = 4000\left\{ {{{\left[ {1 + \dfrac{5}{{100}}} \right]}^N} - 1} \right\}$
Taking 4000 on the LHS side and dividing 630.50 by 4000, we get-
$\dfrac{{630.50}}{{4000}} = {\left[ {1 + \dfrac{1}{{20}}} \right]^N} - 1$
Adding the terms inside bracket and taking 1 on the LHS, we get-
$
  \dfrac{{630.50}}{{4000}} + 1 = {\left[ {\dfrac{{21}}{{20}}} \right]^N} \\
  \dfrac{{4630.50}}{{4000}} = {\left[ {\dfrac{{21}}{{20}}} \right]^N} \\
 $
Now solving further, we get-
$\dfrac{{9261}}{{8000}} = {\left[ {\dfrac{{21}}{{20}}} \right]^N}$
Now 9261 is the cube of 21 and 8000 is the cube of 20,
${\left[ {\dfrac{{21}}{{20}}} \right]^3} = {\left[ {\dfrac{{21}}{{20}}} \right]^N}$
Comparing both the terms we get-
$N = 3$
So, after solving the above equations, we get the time period as 3 years.
Hence the time is 3 years, when the principal amount of Rs.4000 produces compound interest of Rs.630.50 with rate of interest 5%.

Note: Whenever this type of question appears then always first write down the given things in the question. This is a very easy way to approach the question. Remember the formula of compound interest as mentioned in the solution which is $CI = P\left\{ {{{\left[ {1 + \dfrac{R}{{100}}} \right]}^N} - 1} \right\}$, put the values of the principal amount P , the compound interest CI, and the rate of interest R to find the value of time in years.