A 25 year old engineer is opening an IRA account at a bank. Her goal is to accum

Question

A 25 year old engineer is opening an IRA account at a bank. Her goal is to accumulate $1million dollar in the account by the time she retires from work in 40 years. The bank manager estimates she may expect to receive 8% nominal interest, compounded quarterly, throughout the 40 years. The engineer believes that her income will increase at a 7% annual rate during her career. She wishes to start her IRA with a as low a deposit possible and increase it at a 7% per year. Assuming end of year deposits, how much she deposit the first year?

Explanation / Answer

Let the first year amount be X

next year amount is (1.07)X and so on

The total amount after 40 years will be
= (1.02)^160X + (1.02)^156(1.07)X + (1.02)^152(1.07)^2X + .... (1.02)^4(1.07)^39X
= 765.794X (I used excel to compute the sum, you can also use the Geometric progression sum formula to compute this)

765.79X = 1,000,000
X = 1,000,000/765.79 = 1,305.84

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