When a sum of money is put on loan for one and a half years at a rate of 20%,…

Step-by-Step Solution
To find the principal (P), we calculate the compound interest for both scenarios and find the difference.

Given Data:

Principal = P

Annual Rate = 20%

Time = 1.5 years (or 3 half-years)

Scenario 1: Annual Compounding

For the first year, interest is compounded annually: P * (1 + 0.2) = 1.2P.

For the remaining half-year, interest is calculated at half the annual rate (20% / 2 = 10%): 1.2P * (1 + 0.1) = 1.32P.

Interest = 1.32P - P = 0.32P.

Scenario 2: Half-Yearly Compounding

The rate per half-year is 20% / 2 = 10% = 0.1.

There are 3 half-year periods in 1.5 years.

Amount = P * (1 + 0.1)³ = P * (1.331) = 1.331P.

Interest = 1.331P - P = 0.331P.

Calculate the Difference:

Difference in interest = 0.331P - 0.32P = 0.011P.

Given that the difference is 264:
0.011P = 264
P = 264 / 0.011
P = 24,000