To calculate how much money Lynne will have in her IRA when she retires at age 65, we need to use the formula for the future value of an ordinary annuity.
The formula is: FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value
P = Payment amount per period
r = Interest rate per period
n = Total number of periods
Based on the given information:
P = $150 (the payment amount per month)
r = 5.5% annual interest rate, compounded monthly (which means the monthly interest rate is 5.5% / 12)
n = (65 years - 25 years) * 12 months per year
Now, let's plug in the values into the formula and calculate the future value:
n = (65 - 25) * 12 = 480 (months)
r = 5.5% / 12 = 0.00458 (monthly interest rate)
FV = $150 * [(1 + 0.00458)^480 - 1] / 0.00458
Calculating this value, FV ≈ $265,309.
Therefore, Lynne will have approximately $265,309 in her IRA when she retires at age 65.