i used the following financial calculator.
https://arachnoid.com/finance/
Joe plans to deposit $600 at the end of each quarter into an account paying 7.4% interest, compounded quarterly, for 13 years. He will then leave his balance in the account, earning the same interest rate, but make no further deposits for 32 years.
the results of my calculations are shown below:
my inputs were:
present value = 0
future value = 0
number of time periods = 13 * 4 = 52
payment amount = -600
interest rate percent per time period = 7.4 / 4= 1.85
payments are made at the end of each time period.
my output was future value = 51698.03
at the end of the 13 years, joe has 51,698.03 in his account.
this is deposited for another 32 years, at which time joe has 540,115.03.
the results of my calculations are shown below:
my inputs were:
present value = -51698.03
future value = 0
number of time periods = 32 * 4 = 128
payment amount = 0
interest rate percent per time period = 7.4 / 4 = 1.85
payments made at end of time period are irrelevant for this calculation.
my output was future value = 540115.03
Sarah plans to save nothing during the first 13 years and then begin depositing $600 at the end of each quarter in an account paying 7.4% interest, compounded quarterly for 32 years.
at the end of the 13 years, sarah has nothing.
she then deposits 600 at the end of each quarter for 32 years.
at the end of the 32 years, sarah has 306,405.32.
the results of my calculations are shown below:
my inputs were:
present value = 0
future value = 0
number of time periods = 32 * 4 = 128
payment amount= -600
interest rate percent per time period = 7.4 / 4 = 1.85
payment made at end of each time period.
my output was future value = 306405.32
joe has more.
why?
it might be useful to look at the quarterly cash flows from when the 32 year period starts.
joe starts it with 51,698.03
sara starts it with nothing.
here's a series of pictures of what's happening.
sarah's remaining balance never catches up to joe's remaining balance.
even in the 128th time period, joes's net gain from the previous remaining balance is 9810.63, while sarah's net gain (interest plus payment) from the previous remaining balance is 6154.64.