Joe's starting salary as a mechanical engineer is around $80,000. 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 7% annual return over the course of his career, what can Joe expect at retirement?

Since Joe is planning to place a total of 10% of his salary each year in the mutual fund, first deposit will be 80,000*0.1=8,000

For the calculation we should use geometric gradient series formula. But first of all, we need to understand what is geometric gradient series.

So, geometric gradient series are the cash flow series which decreases or increases over time by a particular percentage. They are also called the compound growth.

P=A1[ (1 - (1+g) ^n (1+i) ^ (-n) ] / (i-g)

A1 - initial payment

n - number of years

i - interest rate

g - gradient rate

In this case, salary increases by 5% each year and mutual fund will average 7% annual return over the course of his career.

Also, we know the Future Value formula: FV=PV (1+I) ^n

So, P=8,000 [ 1 - (1+0.05) ^30 (1+0.07) ^ (-30) ] / (0.07-0.05) =

= 8000 * [1 - (4.321) (0.131) ]/0.02 = 8000*21.611 = 172,895.6

Now that we know the present worth, we need to find the Future Value

FV = 172,895.6 * (1+0.07) ^30 = 1,316,125