Marc Egleston MTH 113 Ouiz \#5 1) Suppose you have $\$ 25,000$ to invest in an account with an annual interest rate of $3.9 \%$ compounded weekly. How many years would it take for the investment to be worth $\$ 60,000$ ? Round your answer to the nearest tenth of a year

Step 1 ：Given that you have $25,000 to invest in an account with an annual interest rate of 3.9% compounded weekly, we need to find out how many years it would take for the investment to be worth $60,000.

Step 2 ：This is a compound interest problem. The formula for compound interest is \(A = P(1 + r/n)^{nt}\), where A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Step 3 ：In this case, we know A ($60,000), P ($25,000), r (3.9% or 0.039), and n (52 weeks in a year), and we need to solve for t.

Step 4 ：We can rearrange the formula to solve for t: \(t = \frac{\log(A/P)}{n \cdot \log(1 + r/n)}\).

Step 5 ：By substituting the known values into the formula, we can solve for t.

Step 6 ：Final Answer: It would take approximately \(\boxed{22.5}\) years for the investment to be worth $60,000.