# Joe's starting salary as a mechanical engineer is around $90,000. Joe is planning to place a...

## Question:

Joe's starting salary as a mechanical engineer is around $90,000. Joe is planning to place a total of 10% of his salary each year in the mutual fund. Joe expects a 5% salary increase each year for the next 30 years of employment.

If the mutual fund will average 8% annual rate of return over the course of his career, what can Joe expect at retirement?

## Future Value of Growing Annuity:

Annuity is a series of periodic payment of equal amount and equal interval. Therefore, a growing annuity is a series of periodic payment with an increasing payments but still at equal interval. The future value is the value of money at the end of the term.

{eq}\displaystyle \text{Future value of annuity (FVGA) } = C * \frac{(1 + r)^{t} - (1 + g)^{t}}{r - g} {/eq}

## Answer and Explanation:

**At retirement, Joe can receive $2,703,428.86**

{eq}\displaystyle \text{Future value of annuity (FVGA) } = C * \frac{(1 + r)^{t} - (1 + g)^{t}}{r - g} {/eq}

This is where:

*C*is the required payments*r*is the interest rate*t*is the period*g*is the growth

{eq}\displaystyle \text{Future value of annuity (FVGA) } = 9,000 * \frac{(1 + .08)^{30} - (1 + .05)^{30}}{.08 - .05} = 2,703,428.86 {/eq}

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