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Finance Problem: Future value of an annuity?

02 Jun

Your client is 40 years old, and she wants to begin saving for retirement, with the first payment to come one year from now. She can save 5,000 per year, and you advise her to invest it in the stock market, average return of 9%.

I figured out that at 65 she would have saved: $423,504.48. At 70 she would save: 681,537.69.

The question then asks if she expects to live for 20 years in retirement if she retires at 65 and 15 years if she retires at 70, at the same interest rate….how much could she withdraw at the end of each year after retirement at each retirement age?

I just need some help in the right direction for the final part of this problem. Thanks in advance.

 
3 Comments

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  1. gaken2000

    June 2, 2010 at 1:41 pm

    Well I don’t know the exact mathematical formula involved, but there is a function in EXCEL that will get you pretty close. It’s called PMT (for payment) and is used for calculating the payment on a loan. However it will work for an annuity as well. You would enter your present value at age 65 or 70 (as a negative number, not sure why), your ending value, which would be zero, the number of periods (15 or 20), and the interest rate. The function then calculates the amount you can withdraw per year.

     

  2. spitfiredd

    June 2, 2010 at 1:56 pm

    The first part of the question you were solving for your Future Value.

    Those are right by the way.

    The second part you are solving for PMT.

    Assume that the FV that you solved for in the first part of the question are now your PV and you FV is 0 (basically when you die you have no money left over).

    Both you n and i are given.

    Hope that helps.

     

  3. havo_FINA4242

    June 2, 2010 at 2:44 pm

    If you have a financial calculator you can input these values for your payment: At 65

    N= 20
    I/Y=9%
    PV=423,504.48
    FV=0 ——calculate payment

    At 70
    N=15
    I/Y=9%
    PV=681,537.69
    FV= 0—-calculate payment
    or you can do it on paper with the following formula:

    Yearly payment= future value * ((interest rate (.09)*((1+ interest rate)(raised to the n years))/(((1+interest rate)(raised to the n year)-1) or the following using the numbers for retiring at 65:

    Yearly payment= $423,504.48*((.09*((1.09)^20))/((1.09^20) -1)

    Hope this helps