## Related questions with answers

An engineer graduates at age 22, and she gets a job that pays $60,000 per year. She wants to invest enough to fund her own retirement without relying on an employer pension program or Social Security. Her goal is to have$1 million saved for retirement at age 67. She is relatively confident that her investments will earn an average interest rate of at least 4% per year. (а) Assume that she makes equal annual deposits starting on her 23$^{rd}$ birthday and continuing through her 67$^{th}$ birthday. How much must she invest each year to meet her goal? (b) Suppose she invests the same amount from part (a) every year starting on her 33$^{rd}$ birthday. How much money will she have in the account on her 67$^{th}$ birthday under this scenario?

Solution

Verified#### a.

She wants $F={{\$}} 1,000,000$ as the compound amount of a uniform series of deposits (of A dollars),

over $45$ compounding periods,

(we count 23rd birthday as t=1, 24th as t=2, .... 67th as t=45),

at $i=4\%$ per period.

$\begin{align*} A&=F(A/F, i, n) \\ & =1,000,000(A/F, 4\%, 45)\\ & =1,000,000(0.00826)\\ & ={{\$}} 8260 \end{align*}$

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