SOLUTION: Best Motors has hired Robert Trent as its new president. Terms included the company’s agreeing to pay retirement benefits of $17,900 at the end of each semiannual period for 12 yea

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Question 1113633: Best Motors has hired Robert Trent as its new president. Terms included the company’s agreeing to pay retirement benefits of $17,900 at the end of each semiannual period for 12 years. This will begin in 4,015 days. If the money can be invested at 8% compounded semiannually, what must the company deposit today to fulfill its obligation to Robert?
Found 3 solutions by solver91311, ikleyn, MathTherapy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Posing the same question several times in a row is not going to improve your chances of getting your question answered. In fact, in this case, you have created the opposite effect.

John

My calculator said it, I believe it, that settles it
Answer by ikleyn(52775)   (Show Source): You can put this solution on YOUR website!
.
I will interpret the condition in this way: 

    1)  We have first the period of    = 11 years,  when the initial deposit of X dollars grows at  8%  compounded semiannually.


    2)  Then the second period starts,  when the company withdraw  $17900 semiannually for  12 years to fulfill its obligation to Robert.

        During this period of  12 years the rest of the account is still compounded at  8% semiannually, 
        and at the end of the  12 years period the amount vanishes.

The condition does not formulate all these details,  so,  from one side,  it is my own interpretation / (fantasy).

From the other side,  only this interpretation makes the problem really interesting,  and it is major reason,  why I start to work on it.


Solution 

1.  After 11 years, the initial deposit of X dollars becomes

    P =  = .



2.  Then the following next 12 years period we have the ordinary annuity plane with the NEGATIVE semiannual deposit (= withdraw) of $17900.

    So, the usual ORDINARY ANNUITY PLAN formula works with the negative deposit of 17900 dollars:

   
    P =  = .


    So your equation to find X is THIS:


        = .


       x*2.369919 = 279502.6  =====>  X =  = 117937.60.


Answer.  Under the given condition and interpretation the initial deposit the company must make TODAY is  117937.60 dollars.

Solved.

----------------
See the lesson
    - Ordinary Annuity saving plans and geometric progressions
in this site.

================

I absolutely agree with John in that you do not need copy your post many times - it only annoys/irritates the tutors and works against your best interests.



Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
Best Motors has hired Robert Trent as its new president. Terms included the company’s agreeing to pay retirement benefits of $17,900 at the end of each semiannual period for 12 years. This will begin in 4,015 days. If the money can be invested at 8% compounded semiannually, what must the company deposit today to fulfill its obligation to Robert? 
If the interest rate of 8% were to remain the same, amount needed to pay out $17,900 every 6 months for 12 years, or for 24 periods, would be: $272,920.64. 

This is your FUTURE VALUE, or the amount needed in 4,065 days, or in 

The PRESENT VALUE, based on a FUTURE VALUE of $272,920.64, an interest rate of 8%, semi-annual compounding periods, and time of 11 years () = .

This is the required deposit, TODAY!! 

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