Question

Find the amount and compound interest on ₹.18750 after 3 years, compounded annually, the rates of interest being $ 8\% $ p.a. $ 10\% $ p.a. and $ 12\% \,p.a. $ during the first year, second year and third year respectively.

Answer 1

Hint: Here, we first use formula to find amount using given value of principal and three different rates for three years and then using it on finding difference of the amount with given principal we can find compound interest on given amount and hence solution of required problem.
Formulas used: $ A = P\left( {1 + \dfrac{{{R_1}}}{{100}}} \right)\left( {1 + \dfrac{{{R_2}}}{{100}}} \right)\left( {1 + \dfrac{{{R_3}}}{{100}}} \right),\,\,\,C.I. = A - P $

Complete step-by-step answer:
Given,
Principal = ₹. $ 18750 $
And the rate of three years is given as $ 8\% $ p.a. $ 10\% $ p.a. and $ 12\% \,p.a. $ during the first year, second year and third year respectively.
Time = $ 3\,years $
We know that amount in case of compound interest when rate is different for year by year is given as:
 $ A = P\left( {1 + \dfrac{{{R_1}}}{{100}}} \right)\left( {1 + \dfrac{{{R_2}}}{{100}}} \right)\left( {1 + \dfrac{{{R_3}}}{{100}}} \right) $
Here, P is the principal, $ {R_1},{R_2}\,\,and\,\,{R_3} $ are rates for three given years respectively.
Substituting values in above formulas we have,
 $
  A = 18750\left( {1 + \dfrac{8}{{100}}} \right)\left( {1 + \dfrac{{10}}{{100}}} \right)\left( {1 + \dfrac{{12}}{{100}}} \right) \\
   \Rightarrow A = 18750\left( {1.08} \right)\left( {1.01} \right)\left( {1.12} \right) \\
   \Rightarrow A = 22906.8\left( { \approx 22907} \right) \;
  $
Hence, from above we see that the amount of ₹. $ 18750 $ is ₹. $ 22907 $ .
Therefore, compound interest on a given amount can be calculated by calculating the difference of amount and principal given.
 $
   \Rightarrow C.I. = A - P \\
   \Rightarrow C.I. = 22907 - 18750 \\
   \Rightarrow C.I. = 4157 \;
  $
Hence, from above we see that amount and compound interest on amount of ₹. $ 18750 $ are ₹. $ 22907 $ and ₹. $ 4157 $ respectively.
So, the correct answer is “ ₹. $ 18750 $ are ₹. $ 22907 $ and ₹. $ 4157 $ ”.

Note: To find amount in case of compound interest we can used formula which is given as $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $ but here in this problem instead of one rate there are three different rates for three different years. So we use other formulas instead of standard formulas and then to find the value of C.I. we calculate the difference of amount and principal and hence the required solution of given problem.