Question 1202829: Jennifer is the owner of a video game and entertainment software retail store. She is currently planning to retire in 30 years and wishes to withdraw $15,000/month for 20 years from her retirement account starting at that time. How much must she contribute each month for 30 years into a retirement account earning interest at the rate of 4%/year compounded monthly to meet her retirement goal? (Round your answer to the nearest cent.)
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Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the assumption is that the retirement account is also earning 4% per year compounded monthly as well.
without knowing that interest rate the retirement account is earning, there is no way to determine how much is needed.
under that assumption, the present value of 15000 at the end of each month for 20 years at an interest rate of 4% per year compoundd monthly, would be equal to 2,475,327.87.
that becomes the future value of the next analysis.
the payment at the end of each month for a future value of 2,475,327.87 for 30 years at 4% per year compoounded momthly is equal to 3566.5.
here are the results from the analysis using the calculator at https://arachnoid.com/finance/
in the first analysis, the inputs are:
future value = 0
payment at the end of each time period = 15,000
interest rate per time period = 4/12 = .33333333333.....%
number of time periods = 20 * 12 = 240 months
output is present value.
in the second analysis, the inputs are:
future value = present value from previous analysis.
interest rate per time period = same as for first analysis.
number of time periods = 30 * 12 = 360 months
present value = 0
the calculator assumes that money going out will be negative and money coming in will be positive.
because of that, the payment at the end of each month in second analysis is shown as positive and the present value is shown as negative, and the future value in the second analysis is shown as positive while the payment at the end of each month is negative.
an excel analysis shows the month by month transactions for key events.
the first is the strt of the 30 year investment period.
the second is the end of the 30 year investment period and the strt of the 20 year withdrawal period.
the last is the end of the 20 year withdrawal period.
there are 600 months in total.
360 months for the investment period.
240 months for the withdrawal period
the procedure is:
the remaining balance from the previous time period is multiplied by 1 + the interest rate per month and then the investment is added to it for the investment period, while the withdrawl is subtracted from it for the withdrawal period.
the investment per time period is 3566.5.
the withdrawal per time period is 15000.
let me know if you have any questions.
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