Question

On what sum will the compound interest at 5% per annum for 2 years compounded annually be Rs 164?

Answer 1

Let the sum be Rs x.
We know that: 
CI = A - P
\[ = P \left( 1 + \frac{R}{100} \right)^n - P\]
\[ = P\left[ \left( 1 + \frac{R}{100} \right)^n - 1 \right]\]
\[164 = x\left[ \left( 1 + \frac{5}{100} \right)^2 - 1 \right]\]
\[164 = x\left[ \left( 1 . 05 \right)^2 - 1 \right]\]
\[x = \frac{164}{0 . 1025}\]
\[ = 1, 600\]
Thus, the required sum is Rs 1, 600.