To solve this problem, we need to use the compound interest formula, which is:
A = P(1 + r/n)^(nt)
where:
A is the final amount
P is the principal amount
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time (in years)
We are given:
P = $8,000,000
r = 12% = 0.12
n = 2 (compounded half-yearly)
t = 2.5 years
First, we need to calculate the total number of compounding periods over 2.5 years at a half-yearly rate:
2.5 years * 2 = 5 compounding periods
Now, we can plug in the values into the formula:
A = 8,000,000(1 + 0.12/2)^(2*5)
A = 8,000,000(1.06)^10
A = 8,000,000(1.790847)
A = $14,326,776.28
The final amount after 2.5 years is $14,326,776.28.
To find the compound interest earned, we need to subtract the principal amount from the final amount:
Compound Interest = Final Amount - Principal
Compound Interest = $14,326,776.28 - $8,000,000
Compound Interest = $6,326,776.28
Therefore, the compound interest earned over a period of 2 1/2 years at 12%, if it is compounded half-yearly, is $6,326,776.28.