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​Joe's starting salary as a mechanical engineer is around ​$100 comma 000. Joe is planning to place a total of 13​% of his salary each year in the mutual fund. Joe expects a 5​% salary increase each year for the next 25 years of employment. If the mutual fund will average 11​% annual return over the course of his​ career, what can Joe expect at​ retirement?

Respuesta :

Answer:

$ 2,209,797.96

Explanation:

Given:

Salary = $100,000

Salary investment rate = 13%

Salary increase rate(g) = 5%

number of year = 25

Annual rate of return(i) = 11%

Calculation:

Salary invested = $100,000*13% = $13,000

calculation of present worth

[tex]P=A[\frac{1-(1+g)^n(1+i)^{-n}}{i-g}] \\P=13000[\frac{1-(1+0.05)^{25}(1+0.11)^{-25}}{0.11-0.05}] \\P=13000[\frac{1-(1.05)^{25}(1.11)^{-25}}{0.06}] \\P=13000[\frac{1-(3.386354)(0.073608086)}{0.06}]\\\\P=13000[\frac{1-0.249263}{0.06}]\\\\ P=13000[12.5122827]\\\\\\P= 162,659.675[/tex]

[tex]Future worth = P(1+i)^n\\ = 162,659.675(1+0.11)^{25}\\ = 2,209,797.96[/tex]

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