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Thread: Help with Annuity

  1. #1

    Help with Annuity

    I'm not sure what formulas to use. If you know how to do it using excel that would be great, if not I'll be happy to learn the old fashioned way.
    Thanks

    Funding Jill Moran’s Retirement Annuity

    Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jill Moran. Ms. Moran, by contract, will retire at the end of exactly 12 years. Upon retirement, she is entitled to receive an annual end-of-year payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20-year period, the annual payments will pass to her heirs. During the 12-year “accumulation period,” Sunrise wishes to fund the annuity by making equal, annual, end-of-year deposits into an account earning 9% interest. Once the 20-year “distribution period” begins, Sunrise plans to move the accumulated monies into an account earning a guaranteed 12% per year. At the end of the distribution period, the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and that the first distribution payment will be received at the end of year 13.
    To Do:
    a. Draw a time line depicting all of the cash flows associated with Sunrise’s view of the retirement annuity.
    b. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?
    c. How large must Sunrise’s equal, annual, end-of-year deposits into the account be over the 12-year accumulation period to fund fully Ms. Moran’s retirement annuity?
    d. How much would Sunrise have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period?
    e. How much would Sunrise have to deposit annually during the accumulation period if Ms. Moran’s retirement annuity were a perpetuity and all other terms were the same as initially described?

  2. #2
    Senior Member
    Join Date
    Sep 2012
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    Quote Originally Posted by Kathymathy View Post
    I'm not sure what formulas to use. If you know how to do it using excel that would be great, if not I'll be happy to learn the old fashioned way.
    Thanks

    Funding Jill Moran’s Retirement Annuity

    Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jill Moran. Ms. Moran, by contract, will retire at the end of exactly 12 years. Upon retirement, she is entitled to receive an annual end-of-year payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20-year period, the annual payments will pass to her heirs. During the 12-year “accumulation period,” Sunrise wishes to fund the annuity by making equal, annual, end-of-year deposits into an account earning 9% interest. Once the 20-year “distribution period” begins, Sunrise plans to move the accumulated monies into an account earning a guaranteed 12% per year. At the end of the distribution period, the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and that the first distribution payment will be received at the end of year 13.
    To Do:
    a. Draw a time line depicting all of the cash flows associated with Sunrise’s view of the retirement annuity.
    b. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?
    c. How large must Sunrise’s equal, annual, end-of-year deposits into the account be over the 12-year accumulation period to fund fully Ms. Moran’s retirement annuity?
    d. How much would Sunrise have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period?
    e. How much would Sunrise have to deposit annually during the accumulation period if Ms. Moran’s retirement annuity were a perpetuity and all other terms were the same as initially described?
    Please read on the Admin Board the post entitled "Read Before Posting."

    What do you find confusing about this problem? It is very hard to help you if we do not know what your exact difficulty is.

    What is a present value?

    What is an annuity?

    Does your book have a formula for the present value of an annuity?

    Does your book have a formula to turn a future value into a present value?
    Last edited by mmm4444bot; 11-28-2012 at 06:14 PM.

  3. #3
    Elite Member
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    Location
    Ottawa, Ontario
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    Code:
    0                        .00
    1    d                    ? (interest = 9%)
    2    d                    ?
    3    d                    ?
    ...
    12   d                    x
    13  -20,000.00            ? (interest = 12%)
    14  -20,000.00            ?
    ...
    32  -20,000.00          .00
    You need to find x, which is amount required to permit
    20 payments of $20,000, while earning 12%.

    If that thoroughly confuses you, then you're not ready for this...
    I'm just an imagination of your figment !

  4. #4
    I think I figured it out!
    I used excel to do it
    For
    B: PV of annuity = $313,716.63
    C:
    $15,576.24
    D: $14,670.43
    E: $17,377.73
    thanks for the help!

  5. #5
    Elite Member
    Join Date
    Feb 2004
    Location
    Ottawa, Ontario
    Posts
    12,138
    Your (or Excel's?) posted answers are correct; looks like this:
    Code:
    YEAR    DEPOSIT    INTEREST(9%)     BALANCE
    1      15,576.24          .00      15,576.24
    2      15,576.24     1,401.86      32,554.34
    ...
    12     15,576.24    24,617.10     313,716.68
    YEAR    PAYMENT    INTEREST(12%)    BALANCE
    13    -42,000.00    37,646.01     309,362.69
    ...
    31    -42,000.00     8,517.91      37,499.94
    32    -42,000.00     4,500.06            .00
    I'm a little puzzled at you're mention of Excel:
    are you saying this was done for you by an Excel utility?

    If so, what have you gained/learned? Nothing, right?
    I'm just an imagination of your figment !

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