If the compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 420, what will be the simple interest on the same sum of money at the same rate for 3 years?

To solve this problem, we first need to understand the difference between compound interest and simple interest.

Compound interest is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. The formula for compound interest is:

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

Where: A = the future value of the investment/loan, including interest P = principal investment amount (the initial deposit or loan amount) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested or borrowed for, in years

Given in the problem: P = unknown (we're trying to find this) r = 10% per annum = 0.10 n = compounded annually = 1 t = 2 years A = P + interest = P + Rs. 420

We can plug these values into the formula and solve for P:

P + 420 = P (1 + 0.10/1)^(1*2) P + 420 = P (1.10)^2 P + 420 = P * 1.21 420 = P * 1.21 - P 420 = P * 0.21 P = 420 / 0.21 P = Rs. 2000

Now that we know the principal amount, we can calculate the simple interest for 3 years. The formula for simple interest is:

I = Prt

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

Plugging in the values we know:

I = 2000 * 0.10 * 3 I = Rs. 600

So, the simple interest on the same sum of money at the same rate for 3 years is Rs. 600.