A man earned interest of Rs. 1,050 on investing a certain sum at compound interest of 10% p.a., compounded annually for 2 years. Find the interest earned by him when the same sum is invested at simple interest of 8% p.a. for 3 years. a. RS 1100 b. RS 1200 c. RS 1020 d. RS 1000

To solve this problem, we first need to find the principal amount using the formula for compound interest. The formula for compound interest is:

A = P (1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

Given in the problem: A = Rs. 1,050 (the interest earned) + P (the principal, which we're trying to find) r = 10% per annum = 0.10 (in decimal) n = 1 (since it's compounded annually) t = 2 years

We can rearrange the formula to solve for P:

P = A / (1 + r/n)^(nt)

Substituting the given values:

P = 1050 / (1 + 0.10/1)^(1*2) P = 1050 / (1.10)^2 P = 1050 / 1.21 P = Rs. 867.76 approximately

Now, we can find the simple interest earned when this principal is invested at 8% per annum for 3 years. The formula for simple interest is:

I = Prt

Where: I = the interest P = the principal amount r = annual interest rate (in decimal) t = time the money is invested for in years

Substituting the values:

I = 867.76 * 0.08 * 3 I = Rs. 208.26 approximately

So, the interest earned by him when the same sum is invested at simple interest of 8% p.a. for 3 years is not listed in the options provided. There seems to be a mistake in the problem or the options.