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Question 1103757: You want to be able to withdraw $40,000 from your account each year for 25 years after you retire. If you expect to retire in 15 years and your account earns 6.6% interest while saving for retirement and 5.6% 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 greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
I will work the same problem but with different numbers, to show you the process. Then you can practice using the process with your numbers.
Here is my similar problem:
You want to be able to withdraw $50,000 from your account each year for 25 years after you retire. If you expect to retire in 20 years and your account earns 5.5% interest while saving for retirement and 4.5% interest while retired...."
a) How much will you need to have when you retire?
This is a present value problem: you want to know how much you will need to have at the beginning (of retirement) to be able to withdraw $50,000 each year for 25 years. The present value formula with an annual interest rate r and n periodic withdrawals each of amount A is
(NOTE: In this part of the problem, we are making withdrawals once a year, so the interest rate in the calculation is the annual interest rate.)
With the numbers in my example, the formula is
You will need $741,410.45 in the account when you retire in order to be able to withdraw $50,000 for 25 years.
***NOTE***
I showed every step of the calculation; I of course used a calculator to perform the calculations. I have seen students try to enter the entire formula into their calculators to get the answer; it is very easy to get parentheses in the wrong places. Unfortunately, many students trust their calculators, so if they get an answer that says they need $47.6 million in their account in order to be able to withdraw $50,000 a year for 25 years, they believe it.
The numbers at every stage should have some meaning; if your numbers are not similar, then you are not entering the calculations correctly on your calculator.
The calculation (1+r)^-n should give a number between 0 and 1; so the next calculation 1 - (1+r)^-n should also give you a number between 0 and 1.
The next number tells you the number of regular withdrawal amounts you should have in the account when you start making the withdrawals. In my example, where I want to take withdrawals for 25 years, the number 14.8282 says the amount I have to have in the account at the beginning of those 25 years is only equal to the amount of less than 15 of those withdrawals -- so that is a good number to see.
b) How much will you need to deposit each month until retirement to achieve your retirement goals?
This is a future value problem: You want to know how much you need to deposit each month for the next 20 years to have the required amount $741,410.45 at the end of those 20 years.
The future value formula for the amount of the regular monthly contribution necessary to accumulate an amount P, in n months with an annual interest rate r, is
(NOTE: In this part of the problem, we are making deposits once a month, so the interest rate in the calculation is the monthly interest rate, which is 1/12 of the annual interest rate.)
With the numbers in my example,
The amount of the monthly deposit you need to make is $1701.94.
Thankfully, at this point we are finished with the ugly formulas and difficult calculations. Everything from here on is simple arithmetic.
c) How much did you deposit into you retirement account?
Answer: $1701.94 each month for 20 years, or 240 months: 
You deposited a total of $408,465.60.
d) How much did you receive in payments during retirement?
Answer: $50,000 a year for 25 years = $1,250,000.
e) How much of the money you received was interest?
The difference between how much you took out and how much you put in: $1,250,000 - $408,465.60 = $843,534.40
Now follow the same steps to work the problem with your numbers.
Be sure to enter the calculations correctly in your calculator, and verify that the numbers you get at each stage are reasonable.
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