Question

The difference between simple interest and compound interest at the rate of 12% on the same amount for 3 years is Rs. 112.32. What is the principal amount if the interest is compounded annually?

• A. Rs. 25000
• B. Rs. 2500
• C. Rs. 50000
• D. Rs. 5000
• E. Rs. 2000

Answer 1

The correct option is B Rs. 2500

Let the principal amount be Rs. x.

Calculating SI:
SI for 1 year at 12% rate is Rs (12/100)x. For 3 years, it will be Rs (36/100)x ------ (1)

Calculating CI:
For 1st year, interest = (12/100)x
For 2nd year, interest = (12/100)x + (12/100)x + (144/10000)x
For 3rd year, interest = (12/100)x + (12/100)x + (12/100)x + (144/10000)x + (144/10000)x + (1728/1000000)x ------ (2)

Subtracting equation 2 from 1 and solving further,
312 × 144 × x/1000000 = 112.32
⇒ x = Rs 2500

Alternative way: Using the formula for difference between CI and SI for 3 years, $\frac{P{R}^2}{{100}^2}(3+\frac{R}{100})$

We can also use the above formula to find the value of P.