Question

Find the rate percent per annum if Rs 2000 amount to Rs 2662 in \[1\frac{1}{2}\] years, interest being compounded half-yearly?

Answer 1

Let the rate of interest be R %.
Then,
\[A = P \left( 1 + \frac{R}{100} \right)^n \]
\[2, 662 = 2, 000 \left( 1 + \frac{R}{100} \right)^3 \]
\[ \left( 1 + \frac{R}{100} \right)^3 = \frac{2, 662}{2, 000}\]
\[ \left( 1 + \frac{R}{100} \right)^3 = 1 . 331\]
\[ \left( 1 + \frac{R}{100} \right)^3 = \left( 1 . 1 \right)^3 \]
\[\left( 1 + \frac{R}{100} \right) = 1 . 1\]
\[\frac{R}{100} = 0 . 1\]
R = 10
Because the interest rate is being compounded half - yearly, it is 20 % per annum .