If 29400 dollars is invested at an interest rate of 7 percent per year, compounded semiannually, find the value of the investment after the given number of years.
(a) 5 years:
Your answer is
(b) 10 years:
Your answer is
(c) 15 years:
Your answer is
Answer
Solving these equations, we find that the value of the investment after 5 years is \(\boxed{41499.44}\) dollars, after 10 years is \(\boxed{58196.26}\) dollars, and after 15 years is \(\boxed{81799.13}\) dollars.
Step 1 ：Given that the principal amount (P) is $29400, the annual interest rate (r) is 7% or 0.07 in decimal, the number of times that interest is compounded per year (n) is 2 (since it's compounded semiannually), and the time the money is invested for in years (t) is 5, 10, and 15 years.
Step 2 ：We can use the formula for future value (FV) which is \(FV = P * (1 + r/n)^{nt}\) to find the future value of the investment after 5, 10, and 15 years.
Step 3 ：Substitute the given values into the formula, we get \(FV = 29400 * (1 + 0.07/2)^{2*5}\), \(FV = 29400 * (1 + 0.07/2)^{2*10}\), and \(FV = 29400 * (1 + 0.07/2)^{2*15}\) for 5, 10, and 15 years respectively.
Step 4 ：Solving these equations, we find that the value of the investment after 5 years is \(\boxed{41499.44}\) dollars, after 10 years is \(\boxed{58196.26}\) dollars, and after 15 years is \(\boxed{81799.13}\) dollars.
