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Math Help - Annuity and FV Question

  1. #1
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    Annuity and FV Question

    Barbara currently has $25,000 in her RRSP. She plans to contribute $4,000 at the end of each year for the next 30 years and then use the accumulated funds to purchase a 25-year annuity making payments at the end of each month.

    In 30 years, the fund from which the annuity is paid will earn 4.5% compounded monthly. What monthly payment will she receive?

    How much should Barbara put away monthly, at 8.2% per annum, compounded monthly, so that she can still be guaranteed the same monthly payments from the 25-year annuity derived in part (a)?
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  2. #2
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    Set it up and do it. What are your efforts?

    Note: It may be helpful to supply the interest rate for the accumulation period.
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  3. #3
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    I am sorry, Actually, I've already solved this sum and just wanted to see if my solution was corrected. here it is:

    1. For calculating the FV of Barbara's saving I've divided her savings into three parts.
    $25000 will grow to 230229 in 30 years
    25000(1.035)^30(1.02)^60

    First stream of annuity of 4000 will grow to 101470 in 15 years
    c*(1+r)^t -1/r
    and then to 332926 in next 15 years

    Second stream of annuity of 4000 for 15 years will grown to 112329

    and total FV will be 675484

    Am I right?
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  4. #4
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    Sorry, I am completely unable to follow what you are doing.

    1) First Accumulation: 1.035, 1.02, Second Accumulation: r is what? Have we the ENTIRE problem statement?

    2) Why 30 years and then another 60?

    3) Why did you stop at 15 years and then start it again for another 15 years? Does the interest rate change? Perhaps this is a clue to #1. Are we at 7% semiannually for 15 years and then 8% quarterly for 15 years?

    4) Why are there two $4000 annuities?

    The first thing that needs to happen is a disclosure of the ENTIRE problem statement. I'm just guessing based on what I see you trying to do. So far, it's not working very well.

    Give it another go.
    Last edited by TKHunny; June 3rd 2008 at 01:02 PM.
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  5. #5
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    Ouch, You are right, I posted part B and C of the problem and then posted the solution to part A. Following is PARt A.

    a) If her RRSP earns 7% compounded semi-annually for the next 15 years and 8% compounded quarterly for the following 15 years, what will its value be at the end of 30 years?
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  6. #6
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    You must learn to be more organized. Separate the pieces logically, but make sure you work the problem as a whole.

    Basic principles suggests the total accumulated value:

    25000*1.035^{30}*1.02^{60} +  4000(1.035^{28}*1.02^{60} + 1.035^{26}*1.02^{60} + ... + 1.02^{60} + 1.02^{54} + 1.02^{50} + ... + 1)

    Now, work on making it more convenient. Once you have it all in front of you, you shouldn't lose track of any pieces.

    25000*1.035^{30}*1.02^{60} + 4000(1.02^{60}*[1.035^{28} + 1.035^{26} + ... + 1] + 1.02^{54} + 1.02^{50} + ... + 1)

    Now, let's look at the pieces.

    Sum1 = 1.035^{28} + 1.035^{26} + ... + 1

    Sum2 = 1.02^{54} + 1.02^{50} + ... + 1

    And we have:

    25000*1.035^{30}*1.02^{60} + 4000(1.02^{60}*Sum1 + Sum2)

    That expression is not nearly as scary as where this all started. Focusing on the basic principles will help you keep track. Let the notation help you keep organized.
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  7. #7
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    You need to improve on your notation.
    “$25000 will grow to 230229” - you clearly rounded this from 230,229.41
    “25000(1.035)^30(1.02)^60” - should be 25000[(1.035)^30](1.02)^60
    “First stream of annuity of 4000 will grow to 101470 in 15 years” - again, rounded from 101,469.64
    “c*(1+r)^t -1/r” should be c*[(1+r)^t –1]/r
    “and then to 332926 in next 15 years” - a not so good rounding from the extremely close approximation of 332,924.9996
    “Second stream of annuity of 4000 for 15 years will grown to 112329” ? you either rounded way too far or a total miscalculation. Either way, you’re over by 1,642.55
    “and total FV will be 675484” – overstated by 1,643.14
    “Am I right?” – almost. solve the following
    <br />
\left( {1 + r} \right)^1  = \left( {1 + .02} \right)^4 <br /> <br />
for <br />
r<br />
and use it to recalculate your
    “Second stream of annuity of 4000 for 15 years will grow to ?????????”
    p.s. you obviously solved for r already as shown by you calculation of 332926. recheck your computations.
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  8. #8
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    I got a better one!

    A.M. Best Rating: "A" (Excellent)
    Year Founded: 1979
    Total Assets: $68.7 billion

    Term: 5 years (walk away, no annuitization required)
    Interest: 5.1%
    Sales Charge: None
    Minimum Deposit: $35,000
    Maximum Deposit: $500,000 (without Home Office approval)
    Rate Lock Protection: 60 Days

    what will be my amount by 2010? reply at Annuities and Annuity Calculations-Annuity (home)

    ------
    rocketgurl
    http://www.Annuity-Annuity.info
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