Question

Calculate compound interest on Rs.2000 for 2 years at rate 5%.
(a) 105
(b) 200
(c) 205
(d) 2205

Answer 1

Hint: We will first write the formula $A=P{{\left( 1+\dfrac{r}{100} \right)}^{T}}$ for finding the value of amount after adding interest and then we will substitute all the given values in that formula to find the value of amount and then we will subtract it with the principal to get the value of compound interest.

Complete step-by-step answer:
Let’s use the formula $A=P{{\left( 1+\dfrac{r}{100} \right)}^{T}}$ to find the amount after 2 years.
Now substituting the values in the formula $A=P{{\left( 1+\dfrac{r}{100} \right)}^{T}}$ as,
P = 2000
r = 5
T = 2
Hence, we get
$\begin{align}
  & A=2000{{\left( 1+\dfrac{5}{100} \right)}^{2}} \\
 & A=2000{{\left( \dfrac{21}{20} \right)}^{2}} \\
 & A=2205 \\
\end{align}$
Hence, we get the amount = Rs. 2205
Now we will subtract it with principal to get the value of compound interest.
Therefore, we get
$CI=2205-2000=205$
Hence, the value of compound interest is 205.
Therefore option (c) is correct.

Note: One can make the mistake that after finding the amount they might think that is the value of compound interest because that option is also given, so one must be careful that we need to subtract the principal from it to get the final answer. One should also kept in mind that in the formula $A=P{{\left( 1+\dfrac{r}{100} \right)}^{T}}$ we have already divided r by 100, so the value of r should be put in percentage only.