The simple interest on a certain principal amount for 4 years at 10% per annum is half of the compound interest on 1000 for 2 years at 20% per annum. Find the principal amount.

The principal is 550.

Compound interest on 1000 at 20% for 2 years = 1000(1.2^2 - 1) = 1000 x 0.44 = 440.

Half of this is 220.

Simple interest = P x 10 x 4 / 100 = 0.4P.

Set 0.4P = 220.

P = 550.