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Math Help - Annuity Present Value

  1. #1
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    Annuity Present Value

    Hi

    Can someone assist me with this question .Much appreciated.
    Today is your 50th birthday, and you anticipate that you will continue working until your
    65th birthday. You currently have $50,000 in a bank account and $200,000 in shares. You
    plan to add to these savings by the following annual increments:
    i.depositing $2,000 a year for 10 years, and then $4,000 per year, into your bank account, the first deposit to be made today, and the last on your 65th birthday;
    ii.adding $6000 to your share portfolio today, and increasing this amount by 4% per annum with the last addition on your 65th birthday.
    The bank account is expected to earn 5% per annum, and the share portfolio 12% per annum.
    On your retirement aged 65, you intend to deposit all your savings into an investment account that will earn 10% per annum.

    What is the value of your savings on your 65th birthday (after you have made your annual deposit)?
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  2. #2
    MHF Contributor
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    This looks a little tedious, but not particularly difficult. Have you a spreadsheet? Build it a clue at a time and tell us what you get.
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  3. #3
    Junior Member
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    The bank account:
    <br />
50000*(1.05)^{15} + \sum\limits_{t=1}^{10} \left[ 2000 (1.05)^{15-t} \right] + <br />
\sum\limits_{t=11}^{15} \left[ 4000(1.05)^{15-t} \right]<br />

    The shares:
    <br />
200000 + \left[\sum\limits_{t=1}^{15} (6000*1.04^t)*1.12^{15-t} \right]<br />

    The sum of the two above lines would be the value of the total savings at age 65.
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  4. #4
    Newbie
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    My workings thus far.
    Part A
    i) FVAdue= 2000(1.05)^5 1 * 1.05= $11604
    0.05
    then 2000(1.05)^15 1 * 1.05 = $45315
    0.05
    ii) Stuck on this part???? Cannot work out the cash flows.
    $6000 today meaning FVAdue?

    Value of savings on 65th bday?
    $50000(1.05)^15= $103,946
    $200000(1.12)^15= $1,094,714
    2000(1.05)^10 1 * 1.05= $26,414
    0.05
    2000(1.05)^15 1 * 1.05 = $45,315
    0.05
    Stuck on ii) $$$$$$

    Part B

    Yearly withdraws
    =Savings Amount / (1-(1.10)^-20 = ?????
    .10
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