SOLUTION: Hi I have been trying and trying to find out this answer on my own and I just can't figure it out. Will someone help me solve this please? You plan to work for 40 years and the

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Question 1139382: Hi I have been trying and trying to find out this answer on my own and I just can't figure it out. Will someone help me solve this please?
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4400 per month. You have access to an account that pays an APR of 7.2% compounded monthly.
What size nest egg do you need to achieve the desired monthly yield?
Found 2 solutions by rothauserc, MathTherapy:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
The fixed annuity formula is
:
A = (P/r) * [1 -(1+r)^-t], where A is the total amount of the annuity, P is the Payment, r is the interest rate, and t is the time period
:
This problem uses months, therefore you have to divide the annual interest rate by 12 and multiply the number of years by 12.
:
r = 0.072 / 12 = 0.012
:
t = 25 * 12 = 300
:
You are given P = 4400
:
A = (4400/0.012) * (1 -(1+0.012)^-300) = 356430.9636
:
****************************************
Total amount of nest egg is $356,430.96
****************************************
:
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!
Hi I have been trying and trying to find out this answer on my own and I just can't figure it out. Will someone help me solve this please?
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4400 per month. You have access to an account that pays an APR of 7.2% compounded monthly.
What size nest egg do you need to achieve the desired monthly yield?
If I understand this problem, you're looking for the amount you need to have in order to receive $4,400 per month for 25 years, and compounded at 7.2% each year.

If so, then IGNORE the other person's answer.



This works the same way as purchasing a property for a certain price and then making monthly payments. Therefore, you use the formula for the

present value of an ordinary annuity, or: , where: .

To realize your goal of receiving $4,400 per month for 25 years, @ an interest rate of 7.2% per annum, you need to acquire  by the time you're ready to retire. 

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