The difference between compound interest and the simple interest at the same rate of interest R percent per annum on an amount of Rs. 15,000 for two years is Rs. 96. What is the value of R?
Let principal amount be Rs. P, rate of interest R per annum and time of investment T years. Then,
Amount after T years at compound interest = P × (1 + R)T
Amount after T years at simple interest = P × (1 + R×T)
Compound interest after T years is P × (1 + R)T - P
Simple interest after T years is P × (1 + R×T) - P
Here P = 15000, T = 2 years and R = ?
So, according to the question, we have
15000 × ((1+R)2 -1) - 15000 × ((1+2R) -1) = 96
(since, if P, R and T are same, amount with compound interest is always greater than amount with simple interest)
15000×(R2 + 2R) - 15000×(2R) = 96
15000×(R2 + 2R - 2R) = 96
15000×(R2) = 96
R2 = (96÷15000)
R2 = 0.0064
R = 0.08
The correct option is A.