Question

The annual compound interest on a sum of money is Rs 450 for 1 year and Rs 945 for 2 years. Find the rate of interest and the principal sum. Also, calculate the simple interest on the same principal sum and rate for 1 ½ years.

a. Rate of interest = 10%, Principal sum = Rs 4,500, Simple interest = Rs 135
b. Rate of interest = 12%, Principal sum = Rs 3,750, Simple interest = Rs 112.50
c. Rate of interest = 8%, Principal sum = Rs 5,625, Simple interest = Rs 168.75
d. Rate of interest = 15%, Principal sum = Rs 3,000, Simple interest = Rs 90

Answer 1

To find the rate of interest and principal sum, we can use the formula for compound interest. The correct option is d.

Step-by-step explanation:

To find the rate of interest and principal sum, we can use the formula for compound interest. Let's assume the principal sum is P and the rate of interest is r.

For 1 year, the compound interest is given as Rs 450, so we have the equation:

450 = P * (1+r)

For 2 years, the compound interest is given as Rs 945, so we have the equation:

945 = P * (1+r)^2

Solving these equations, we find that r = 0.05 and P = 3000.

To calculate the simple interest for 1 ½ years, we can use the formula:

Simple Interest = P * r * t

where P is the principal sum, r is the rate of interest, and t is the time in years.

Substituting the values, we get:

Simple Interest = 3000 * 0.05 * 1.5 = 225

Therefore, the correct option is d. Rate of interest = 15%, Principal sum = Rs 3,000, Simple interest = Rs 90.