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Question 1031762: Hi, I need help solving this problem. I have excercised everything I know from my notes and research on the internet about how to solve it and I got nothing. My notes don't even explain how to solve this problem fully. I don't know where to start or what formula I should be using. This is my question:
You want to be able to withdraw $25,000 from your account each year for 20 years after you retire. If you expect to retire in 25 years and your account earns 7% interest while saving for retirement and 6.7% interest while retired:
Round your answers to the nearest cent as needed.
a) How much will you need to have when you retire?
b) How much will you need to deposit each month until retirement to achieve your retirement goals
c) How much did you deposit into you retirement account?
d) How much did you receive in payments during retirement?
e) How much of the money you received was interest?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you will start investing your monthly payments on january 1, 2017, and you plan to retire on january 1, 2042
that's exactly 25 years from january 1, 2017.
on january 1, 2042, you need to have enough money in the account to allow you to to withdraw 2083.3333... at the beginning of each month for the next 20 years until december 1, 2062.
the first thing you need to find out is how much money needs to be in the account on january 1, 2042.
you would be using the present value of a payment formula to calculate this.
you can also use a time value of money calculator, if you have one available.
based on my calculations, you will need to have 270,281.0509 dollars in the account on january 1, 2042.
the next thing you need to find out is how much money needs to be put into the account at the beginning of each month from january 1, 2017 until december 1, 2041 so that all the required money is in the account on january 1, 2042.
you would be using the payment for a future value formula to calculate this.
you can also use a time value of money calculator, if you have one available.
based on my calculations, you will need to put 347.8666946 dollars in the account at the beginning of each month until december 1, 2041.
that will give you the required amount of 270,281.0509 by january 1, 2042.
i don't have time to finish this up any more today.
hopefully this will give you an idea of what to do.
you need to get the time points right.
then you need to use the present value of an annuity to find out how much you need to invest at the beginning of your retirement.
then you need to use the annuity for a future value to find out how much you need to invest each month in order to have the required amount at the beginning of your retirement.
there are complications with the financial formulas involving end of month payments versus beginning of month payments.
beginning of month payments is just an adjustment to the end of month payment calculations.
you can do the formulas manually or you can use financial formulas from excel or from a TI Business Analyst II, depending on what you have and what you are allowed to use.
i can't finish up today but will finish up tomorrow or the next day if you wish.
the numbers you need as far as i can see are:
347.8666946 invested at the beginning of each month from now until 25 years from now.
270281.0509 in the account at the beginning of your retirement, from which you will be withdrawing 2083.33333 at the beginning of each month for the next 20 years.
i can provide the details by tomorrow morning or the morning after, hopefully by tomorrow morning.
let me know if you want further informtion regarding this. it takes a little doing to do the calculations, but it takes a little more doing to explain wht's happening and how it's done.
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