Answer: $227,226.51
Explanation:
First, we need to convert the period to weeks.
9 1/2 years = 9.5 years
1 year = 52 weeks
9.5 years = 494 weeks
Next, we can use the formula for the future value of an annuity:
FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)
where:
PMT = payment amount per period
r = annual interest rate
n = number of compounding periods per year
t = number of years
Plugging in the given values:
PMT = $300
r = 0.055 (5.5% expressed as a decimal)
n = 52 (compounded weekly)
t = 9.5 years = 494 weeks
FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)
FV = $227,226.51
Therefore, the future value of the annuity is approximately $227,226.51.