If you could please help me with a detailed solution that would bewonderful. I l

Question

If you could please help me with a detailed solution that would bewonderful. I left my book at home so I don't have any of theformulas.


You are provided with an investment opportunity that provides anannual interest rate over the first 10 years of 7.25%. Afterthat initial period the interest rate is reduced to 5%. Youmake a one time investment of 100,000$. After 20 years youbegin to draw down your investment over a 15 year period (it isstill earning 5%). What is the maximum level withdrawl amountrequired to bring the account balance to zero at the conclusion ofthe 15th year.

Explanation / Answer

first we calculate the accumulated value at the 20th year ofthe initial investment ($100,000),
S=100,000*(1.0725)10*(1.05)10=327,994.08 then assumming the level withdrawal is made annually, S=X*a15    where a15 isdenoted as the present value of an annuity for a period of 15years and a15 = (1-(1.05)-15)/0.05 we found S previously, and thus plug in all the values, we will get X =327,994.08/10.38=31,598.66$ hence , the level withdrawal should be $31,598.66annually

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