Question

Find the compound interest on Rs. 5000 for one year at 4% per annum being compound half yearly.
(a). Rs.200
(b). Rs.202
(c). Rs.204
(d). Rs.208

Answer 1

- Hint: We will solve this equation using the formula \[A=P{{\left( 1+\dfrac{r}{100} \right)}^{(n)(t)}}\] where A is the amount, P is the principle, R is the rate of interest, T is the time of investment and CI is the compound interest.

Complete step-by-step solution -

We are given that the Rate of Interest is 4% per annum and we have to calculate the principal compounded half yearly so we will divide the rate of interest by 2
So, the new rate of interest will be,
$ R=\dfrac{4}{2}\% $
 $ \Rightarrow R=2\% $
Let the amount for the first half will be,

  $ \Rightarrow A=5000{{\left( 1+\dfrac{2}{100} \right)}^{1}} $
 $ \Rightarrow A=5000\left( \dfrac{102}{100} \right) $
$ \Rightarrow A=5100 $
Therefore, the CI for the first year will be Rs. 100
So, the Principle for the second half will be Rs 5100
Now the amount for the second year will be,
 $ \Rightarrow A=5100{{\left( 1+\dfrac{2}{100} \right)}^{1}} $
 $ \Rightarrow A=5100\left( \dfrac{102}{100} \right) $
 $ \Rightarrow A=5202 $

So, the compound interest for the second year will be = 5202 - 5100
Therefore the CI for the second year is Rs 202
So the compound interest for both the half is = 100+ 102
CI = 202
Compound interest for the full year will be Rs 202.

Therefore, the answer of the question will be Rs.202, that is option (b).

Note: The possibility of error in these types of questions would be not calculating the compound interest CI for all the two or three years separately. We should always go for calculating the interest compounded annually separately for each year.