a certain principal amounts to rs 17640 in 2 years at the rate 5 p.c.a. by compound interest. find the amount of the same principal at the rate 10 p.c.a. in 2 years by compound interest.

To solve this problem, we first need to find the principal amount. We know that 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 17640 r = 5% per annum = 0.05 (in decimal) n = 1 (since it's compounded annually) t = 2 years

Substituting these values into the formula, we get:

17640 = P(1 + 0.05/1)^(1*2) 17640 = P(1.05)^2 17640 = P * 1.1025

Solving for P, we find:

P = 17640 / 1.1025 P = Rs 16000

Now, we need to find the amount of the same principal at the rate 10% p.a. in 2 years by compound interest.

Substituting P = Rs 16000, r = 10% per annum = 0.10 (in decimal), n = 1, and t = 2 years into the formula, we get:

A = 16000(1 + 0.10/1)^(1*2) A = 16000(1.10)^2 A = 16000 * 1.21 A = Rs 19360

So, the amount of the same principal at the rate 10% p.a. in 2 years by compound interest is Rs 19360.