Final answer:
To determine the future value of an investment at a compound interest rate of 7.25% per annum compounded half yearly for six years, we use the formula A = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
Step-by-step explanation:
The question asks what the value of an investment would be after six years when invested at a compound interest rate of 7.25% per annum, compounded half-yearly. To find the future value of an investment compounded half-yearly, we use the formula:
A = P(1 + r/n)nt
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the time the money is invested for, in years.
In this scenario, the initial investment (P) is E320750, the annual interest rate (r) is 7.25% or 0.0725 as a decimal, and the interest is compounded half-yearly, which means n is 2. Since the investment is for 6 years, t is 6. Plugging these into the formula, we calculate the future value as follows:
A = 320750(1 + 0.0725/2)2*6
The exact future value can be calculated using a calculator to apply the compounded interest formula.
Note: As the numerical approximation is not provided in this answer, a calculator or a computational tool would be necessary to get the final future value of the investment.