Question

When Compounded quarterly.
(i) $ Rs.{\text{ 6000 at 20% }} $ p.a. for $ 6 $ months
(ii) $ Rs.\,{\text{5000 at 24% }} $ p.a. for $ 9 $ months

Answer 1

Hint: Interest is the amount of money paid for using someone else’s money. Here we will use the formula $ A = P{\left( {1 + \dfrac{R}{4}} \right)^{4n}} $ and compound interest is the difference between the amount and the principal.

Complete step by step solution:
(i) Here we are given,
Principal, $ P = Rs.{\text{ 6000}} $
Rate of Interest, $ R = 20\% = 0.2 $
Term, $ n = 6{\text{ months = 0}}{\text{.5 year}} $
Now, Using the formula $ A = P{\left( {1 + \dfrac{R}{4}} \right)^{4n}} $
Place the values in the above equation –
 $ A = 6000{\left( {1 + \dfrac{{0.2}}{4}} \right)^{4 \times \dfrac{1}{2}}} $
Simplify the above equation
 $
  A = 6000{\left( {1 + 0.05} \right)^2} \\
  A = 6000{\left( {1.05} \right)^2} \\
  A = 6615 \\
  $
Now, the compound interest,
  $
  C.I. = 6615 - 6000 \\
  C.I. = 615{\text{ Rs}}{\text{.}} \\
  $
Similarly,
(ii) Here we are given,
Principal, $ P = Rs.{\text{ 5000}} $
Rate of Interest, $ R = 24\% = 0.24 $
Term, $ n = 9{\text{ months = }}\dfrac{9}{{12}}{\text{ year}} $
Now, Using the formula $ A = P{\left( {1 + \dfrac{R}{4}} \right)^{4n}} $
Place the values in the above equation –
 $ A = 5000{\left( {1 + \dfrac{{0.24}}{4}} \right)^{4 \times \dfrac{9}{{12}}}} $
Simplify the above equation
 $
  A = 5000{\left( {1 + 0.06} \right)^3} \\
  A = 5000{\left( {1.06} \right)^3} \\
  A = 5955.08{\text{ Rs}}{\text{.}} \\
  $
Now, the compound interest,
  $
  C.I. = 5955.08 - 5000 \\
  C.I. = 955.08{\text{ Rs}}{\text{.}} \\
  $

Additional Information:
In other words, present value shows that the amount received in the future is not as worth as an equal amount received today. Always remember the relation among the present value and the principal amount. Always convert the percentage rate of interest in the form of fraction or the decimals and then substitute further for the required solutions. Know the difference between the simple interest method and compound interest method. Simple interest is calculated on the basis of the principal amount whereas the compound interest is calculated on the basis of the principal amount and the interest accumulated in all the previous years of the term period.

Note:
Always convert the percentage rate of interest in the form of fraction or the decimals and then substitute further for the required solutions. Remember the difference between simple interest and compound interest and apply its concept wisely. Compound interest is the interest paid for the interest earned in the previous year. Be good in multiples and do simplification carefully.