SOLUTION: You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round y

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Question 1204351: You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar.
Regular withdrawal: $3400
Interest rate: 5%
Frequency monthly
Time: 28 years
what is the
Account balance: $
- i put 616750 and it was wrong

Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.
You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms.
Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar.
Regular withdrawal: $3400
Interest rate: 5%
Frequency monthly
Time: 28 years
what is the
Account balance: $
- i put 616750 and it was wrong
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


        As this problem is presented in the post,  it uses many smart words,  but essentially,  it is incomplete.

                In other words,  the problem is posed   .

        It is incomplete because it does not specify  WHEN  the withdrawal is made:  at the end or at the beginning of each month.

        Usually, in such problems, withdrawal is at the  BEGINNING  of each month to provide the living expenses;
        but in other problems,  it can be different.

        I solved the problem below under this assumption and got same value as in your post. 


The general formula  A = .


Here A is the initial amount at the account; W is the monthly withdrawn value (at the beginning of each month); 
r is the nominal monthly percentage r = 0.05/12 presented as a decimal;  
p = 1 + r  and n is the number of withdrawing periods (months, in this case).


In this problem,  W = 3400;  the monthly rate is  r = 0.05/12,  
p = 1 + 0.05/12, the number of payment periods (= the number of months) is n = 28*12 = 336.  So


          A =  = 616749.88  dollars.


It is the initial amount.


        If to solve it at the different assumption  (withdrawal is made at the END of each month),
        then the answer is  614190.75 dollars.

Solved.

--------------------

In this site,  there is a group of lessons associated with annuity saving plans and retirement plans.  They are

    - Ordinary Annuity saving plans and geometric progressions
    - Annuity Due saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
    - Withdrawing a certain amount of money periodically from a compounded saving account (*)
    - Miscellaneous problems on retirement plans

From these lessons,  you can learn the subject and can see many other similar solved problems.

The closest lesson to your problem is marked  (*)  in the list.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Think of it like a loan.

You loan the annuity company L dollars at an annual interest rate of 5%, which is roughly equivalent to the monthly rate (5%)/12 = 0.416666667%.
The timespan is 12*28 = 336 months.

The annuity company will then pay you back $3400 per month for 336 months until their balance is paid off.

Let's determine the loan amount
P = (L*i)/(1 - (1+i)^(-n)) <<---------------------------- monthly payment formula
3400 = (L*0.00416666667)/(1 - (1+0.00416666667)^(-336))
3400 = L*0.00553573951128
L = 3400/0.00553573951128
L = 614,190.749595772
L = 614,190.75
L = 614,191

If you loan the company around $614,191, then the company would pay you back payments of roughly $3400 per month for 336 months (equivalent to 28 years).

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If you want to use a TI83 or TI84 calculator, then press the APPS button. Scroll to "Finance". Then go to "TVM Solver".
TVM = time value of money

We'll have these inputsGo back to PV and press the button labeled "alpha", then press the "enter" at the bottom right corner.
This will tell the calculator to solve for the PV entry.
The 0 will change to 614190.7499 which rounds to 614191 when rounding to the nearest dollar.


Here's an emulator of the TI83 TVM solver if you want practice using it, but you forgot your calculator.
https://www.geogebra.org/m/mvv2nus2

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Want to use a spreadsheet?
The command to input would be =PV(0.05/12,336,-3400,0,0)
The template is
PV(rate, nPer, PMT, FV, type)
wherePayments at the beginning of the month would be type = 1. If you went with this option, then it leads to $616,750 which is what you got. However, it appears that your teacher wants payments at the end of the month instead.

Don't forget about the equal sign up front or else the spreadsheet command won't execute. Instead it would be plain text.
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