# The difference between compound interest and the simple interest

Interests
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?

- 8
- 10
- 12
- Cannot be determined due to insufficient data

### Answer

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×(R^{2} + 2R) - 15000×(2R) = 96

15000×(R^{2} + 2R - 2R) = 96

15000×(R^{2}) = 96

R^{2} = (96÷15000)

R^{2} = 0.0064

R = 0.08

**The correct option is A.**