Question 1190657: You expect to retire in 15 years. After you retire, you want to be able to withdraw $2,500 from your account each month for 20 years.
If your account earns 5% interest compounded monthly, how much will you need to deposit each month until retirement to achieve your retirement goals? (Round to the nearest cent.)
I've tried to do this but I think I got the wrong answer
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i get the following:
if the 2500 is taken out at the end of each month, then you will need to invest 179,217.7593 now.
round to the nearest penny to get 179,217.76.
rounding was done only at the end of two separate calculations, the first to find the present value required 15 years from now and the second to find the present that today.
if the 2500 is taken out at the beginning of each month, then you will need to invest 179,964.5 now.
this answer did not need to be rounded to the nearest penny because it was exact to the nearest penny.
i used the texas instrument business analyst ii calculator to get these results.
based on these calculations, you have two possible answers.
the first is 179,217.76 if you assume withdrawals at the end of each month.
the second is 179,964.5 if you assume withdrawals at the beginning of each month.
the method is to find the present value required for the withdrawals starting 15 years from now.
that becomes the future value that you need to bring back to the current time frame.
as an example, assuming end of month payments, i got the amount of the loan required in 15 years to be equal to 378,813.2827...
i then found the present value of that for 15 years to be equal to 179,217.7593 which i rounded to 179,217.76.
the interest rate of 5% per year was divided by 12 to get an interest rate of .41666666...% per month.
number of months for the withdrawal period was 20 * 12 = 240.
number of months for the investment period was 15 * 12 = 180.
HOWEVER !!!!!!
i thought you needed the present value.
it appears you needed the monthly payments.
the other tutor's answer would be correct if you assumed end of month payments during retirement.
that would be 1417.242619 at the end of each month.
if you assumed beginning of month payments during retirement, then the answer should be 1423.147797 invested at the end of each month until retirement.
try 1417.24 and also try 1423.15.
payments are usually made at the end of each month.
withdrawals can sometimes be at the end of each month or at the beginning of each month.
let me know how you did.
theo
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! You expect to retire in 15 years. After you retire, you want to be able to withdraw $2,500 from your account each month for 20 years.
If your account earns 5% interest compounded monthly, how much will you need to deposit each month until retirement to achieve your retirement goals? (Round to the nearest cent.)
I've tried to do this but I think I got the wrong answer
The other person is WRONG!
In 15 years, at the time of retirement, you'll need $378,813.28 in order to withdraw $2,500 per month for 20 years
thereafter, at 5% annual interest, compounded monthly.
To acquire the $378,813.28 in 15 years, you'll need to deposit $1,417.24 per month for 15 years, at 5% annual interest,
compounded monthly.
You wanna check your answers against these?
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