A sum of money lent 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 half-yearly, then the interest rate would be 20%/2 = 10% per half-year.
So, after 2 years, the amount will be P(1 + 0.1)^4 = P(1.1)^4.

If the interest is payable annually, then the interest rate would be 20% per annum.
So, after 2 years, the amount will be P(1 + 0.2)^2 = P(1.2)^2.

According to the given information, the difference between the two amounts is $482.
So, P(1.2)^2 - P(1.1)^4 = 482.

Simplifying the above equation, we get:
1.44P - 1.4641P = 482,
-0.0241P = 482,
P = 482 / -0.0241,
P ≈ -20041.49.

Since the principal amount cannot be negative, we ignore the negative sign.
Therefore, the sum of money lent is approximately $20,041.49.