Summer money lant a sum of money land at compound interest for 2 years at 20% per annum would fetch 482 more if the interest was payable half yearly then it was payable annually. The sum is:

Answer 1

Let's assume the principal amount is P.

If the interest is payable annually, the compound interest for 2 years at a rate of 20% per annum would be:

CI_annual = P(1 + 0.20)^2 = P(1.20)^2

If the interest is payable half-yearly, the compound interest for 2 years would be calculated as:

CI_half_yearly = P(1 + 0.10)^4 = P(1.10)^4

According to the given information, the interest payable half-yearly would fetch $482 more than if it was payable annually:

CI_half_yearly - CI_annual = 482
P(1.10)^4 - P(1.20)^2 = 482
P[(1.10)^4 - (1.20)^2] = 482

Using a calculator, we can find that (1.10)^4 = 1.4641 and (1.20)^2 = 1.44.

P(1.4641 - 1.44) = 482
P(0.0241) = 482
P = 482 / 0.0241
P ≈ $20,033.19

Therefore, the sum of money is approximately $20,033.19.