Question 1121152: A young executive deposits $400 at the end of each month for 4 years and then increases the deposits. If the account earns 7.2%, compounded monthly, how much (to the nearest dollar) should each new deposit be in order to have a total of $400,000 after 25 years?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! as i understand this:
he is investing 400 at the end of each month for 4 years, after which he will be investing a different amount for the next 21 years (total of 25), so that he will have 400,000 dollars at the end of the 25 year investment period.
this is broken up into two pieces.
the first piece is the investment of 400 at the end of each month for 4 years.
the interest rate per year is 7.2%.
divide that by 12 to get the monthly interest rate per month equal to .6%.
the number of years is multiplied by 12 to get the number of months.
your inputs are:
present value = 0
future value = 0
number of time periods = 4 years * 12 months per year = 48 months
payment amount = -400 at the end of each month.
interest rate = 7.2% per year / 12 month in the year = .6% per month.
payment is made at the end of each time period.
click on FV and the calculator tells you how much you have at the end of the 48 month time period.
that amount is 22,174 dollars.
here are the calculator results for that part of this problem.
the next part of this problem is to find out what the payment will be in order 400,000 at the end of 25 years.
the future value of 22,174 from the last part of the problem becomes the present value of -22,174 in the next part of the problem.
the interest rate is the same at .6% per month.
the future value is set to 400,000 dollars.
payments are made at the end of each time period.
the number of time periods is 21 years * 12 months per year = 252 months.
you click on PMT and the calculator tells you that the payments need to be -511.83 at the end of each month.
here are the calculator results for that part of the problem.
note:
you enter the values without any commas.
you enter the present value as negative.
the payment required will come out as negative.
the future value will be positive.
negative means money going out.
positive means money coming in.
the calculator inserts commas where needed in the output display.
i also did this problem in excel to show you the month by month figures for the critical time periods.
i showed the first few months and the last few months.
hopefully that's enough for you to get the flavor of what the indiviedual payments looked like.


the basic formula is that the the remaining balance from the previous time period is multiplied by (1 + .072/12) and then the payment amount is added.
for the first 48 time periods, the payment amount is $400,00
for the last 252 time periods, the payment amount is $511.i83.
you can see that the remaining balance is $400,000 at the end of the 300 time periods (48 + 252 = 300).
each time period is a month.
the calculator i used can be found at https://arachnoid.com/finance/
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