Answer:
Madison will invest during 40 years, since we are not told if the account capitalizes interest monthly, weekly or annually, I will assume the interests are capitalized weekly:
total number of payments = 40 x 52 = 2,080
weekly interest rate =5% / 52 = 0.09615%
future value annuity factor = [(1 + 0.09615%)²⁰⁸⁰ - 1 ] / 0.09615% = 6,637.2376
Madison will have $41 x 6,637.2376 = $272,126.74 by the time she is 68.
If instead she starts to save when she is 56, she will only make 12 x 52 = 624 deposits
we know the future value = $272,126.74
the future value annuity factor = [(1 + 0.09615%)⁶²⁴ - 1 ] / 0.09615% = 854.4573
weekly deposit = $272,126.74 / 854.4573 = $318.48
