Question

Find the compound interest at the rate of $ 14\% $ per annum for $ 1 $ year on the sum of Rs. $ 12,000 $ compounded half-yearly.

Answer 1

Hint: Interest is the amount of money paid for using someone else’s money. There are two types of interest. $ 1) $ Simple Interest and $ 2) $ Compound interest. Interest can be calculated on the basis of various factors. Here we will calculate Amount annually semi-annually and then its difference between the sum value (P). Use formula – $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $ Where A is the amount, P is the Principal amount and R is the rate of interest.

Complete step-by-step answer:
Sum (P) $ = 12,000 $
Rate of Interest, $ = 14\% $ per annum
Since, the rate of interest is compounded half-yearly.
 $ \therefore R = \dfrac{{14}}{2} = 7\% $
Time $ = 1{\text{ year}} $
Since, interest is compounded twice a year, $ n = 2 $
Now,
Amount, $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n} $
Place values in the above equation –
 $ \Rightarrow A = 12000{\left( {1 + \dfrac{7}{{100}}} \right)^2} $
Take LCM (Least common multiple) and simplify
 $ \Rightarrow A = 12000{\left( {\dfrac{{107}}{{100}}} \right)^2} $
Further multiplication and division implies –
 $ \Rightarrow A = 13738.8{\text{ Rs}}{\text{.}} $
Now, the compound Interest $ = Amount{\text{ - Principal (Sum)}} $
Place the values
 $
  C.I. = 13738.3 - 12000 \\
  C.I. = Rs.{\text{ }}1738.8 \;
  $
Hence, the required answer is – the compound interest is $ Rs.\;{\text{1738}}{\text{.8}} $

Note: 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.