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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? Options Rs. 480 Rs. 600 Rs. 540 Rs. 660

Question

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?

Options Rs. 480

Rs. 600

Rs. 540

Rs. 660

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Solution

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

Compound interest for 2 years is calculated as follows:

P(1 + r/100)^2 - P

Where: P = Principal amount (the initial amount of money) r = Annual interest rate (decimal)

Given that the compound interest for 2 years is Rs. 420 and the annual interest rate is 10%, we can set up the following equation:

P(1 + 10/100)^2 - P = 420 P(1.1)^2 - P = 420 P*1.21 - P = 420 0.21P = 420 P = 420 / 0.21 P = Rs. 2000

Now that we have the principal amount, we can calculate the simple interest for 3 years. Simple interest is calculated as follows:

I = Prt

Where: I = Interest P = Principal amount r = Annual interest rate (decimal) t = Time (in years)

Substituting the known values into the equation:

I = 200010/1003 I = Rs. 600

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

This problem has been solved

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