Discussion

When difference between compound and simple interest for three years is Rs. 122 at 5% rate per annum, the principal is ______

Answer: D

\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]

Over three years,

\[ \text{CI} - \text{SI} = P\left[\left(1 + \frac{R}{100}\right)^{3} - 1 - \frac{3R}{100}\right] \]

\[ = P\left[(1.05)^{3} - 1 - 0.15\right] = P(1.157625 - 1.15) = 0.007625P \]

\[ 122 = 0.007625P \quad\Longrightarrow\quad P = \text{Rs. } 16{,}000 \]

Checking: SI = 2400 and CI = \( 16000 \times 0.157625 = 2522 \) - a difference of exactly Rs. 122.

No comment is present. Be the first to comment.

Loading…