Following her 18th birthday, Madison began investing $41 at the end of each week in an account earning 5% per year. She plans to continue making weekly investments until she turns 68. Instead, if she hadn't started investing until she turned 56, how much would she have had to invest each week in order to have the same retirement nest egg at age 68

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

Explanation:

The correct value of inventory:

Year end balance $267,670

Add:

Goods purchased on term FOB shipping point $25,600

Goods sold on terms FOB destination $52,170

Less: Goods purchased on terms FOB destination ($43,630)

Correct inventory as on December 31 $301,810