Question 9

Find the final amount of money in an account after 9 years if $\$ 7,500$ is deposited initially at $4.5 \%$ interest compounded weekly.

Be sure to clearly show your work on your paper!

The final amount is $\$$ - Round answer to 2 decimal places

Step 1 ：Define the variables where P is the principal amount which is $7500, r is the annual interest rate which is 4.5%, n is the number of times interest applied per time period which is 52 weeks in a year, and t is the time the money is invested for which is 9 years.

Step 2 ：Calculate the final amount using the formula for compound interest: \(A = P \times (1 + \frac{r}{n})^{nt}\)

Step 3 ：Substitute the values into the formula: \(A = 7500 \times (1 + \frac{0.045}{52})^{52 \times 9}\)

Step 4 ：Calculate the value of A which gives the final amount of money in the account after 9 years.

Step 5 ：The final amount of money in the account after 9 years is approximately \$11242.80.