Question

Find the amount if Rs 20,000 is invested at 10% p.a. for 3 years.
A. Rs.33111
B. Rs.26620
C. Rs.85500
D. Rs.66699

Answer 1

Hint: In this problem, we need to use the compound interest formula when the interest is compounded annually to obtain the accumulated amount after three years.

Complete step-by-step answer:
The principle is Rs 20,000, annual interest rate is 10% and time is 3 years.
The formula for the calculation of amount \[A\] when the interest is compounded annually is shown below.
\[{\text{A = P}}{\left( {1 + \dfrac{R}{{100}}} \right)^n}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......\left( 1 \right)\]
Here, \[P\]is principal, \[R\]is annual rate of interest and \[n\] is time in years.
Substitute 20,000 for\[P\], 10 for \[R\]and 3 for \[n\] in equation (1) to obtain the accumulated amount after 3 years.
\[\begin{gathered}
  \,\,\,\,\,{\text{A = 20,000}}{\left( {1 + \dfrac{{10}}{{100}}} \right)^3} \\
   \Rightarrow {\text{A = 20,000}}{\left( {1 + \dfrac{1}{{10}}} \right)^3} \\
   \Rightarrow {\text{A = 20,000}}{\left( {\dfrac{{11}}{{10}}} \right)^3} \\
   \Rightarrow {\text{A = 20,000}} \times \dfrac{{11}}{{10}} \times \dfrac{{11}}{{10}} \times \dfrac{{11}}{{10}} \\
   \Rightarrow {\text{A = 20}} \times {\text{11}} \times {\text{11}} \times {\text{11}} \\
   \Rightarrow {\text{A = 26,620Rs}} \\
\end{gathered}\]
Thus, the amount at the end of the 3 years is Rs.26,620.
Hence option B is the correct answer.

Note: Compound interest is the calculation of the interest on the initial principal, which also includes the accumulated interest from the previous time period. Compound interest is also known as interest of interest.