Final answer:
To find out how much will be in the bond after 10 years, you calculate the future value of the investment using the compound interest formula, revealing that you will have approximately $14,859.47.
Step-by-step explanation:
To calculate the amount you will have in 10 years when you invest $10,000 in a governmental bond that pays a 4.0% interest rate compounded semi-annually, you need to use the formula for compound interest: A = P(1 + r/n)^(nt). Here, A is the amount of money accumulated after n years, including interest. P is the principal amount ($10,000), r is the annual interest rate (0.04), n is the number of times that interest is compounded per year (2), and t is the time the money is invested for (10 years).
Using these values, the formula becomes: A = $10,000(1 + 0.04/2)^(2*10). Next, we calculate the value inside the parenthesis (1 + 0.04/2) = 1.02 and then raise it to the power of 20 (1.02^20).
After performing the calculation, we find that A = $10,000 * (1.02^20). So the future value of the investment after 10 years is calculated to be A = $10,000 * (1.485947). Thus, you will have approximately $14,859.47 at the end of 10 years.