This is from an Excel class in Financial Technology. Maybe someone can enlighten me on what the professor did.

The professor had the following cells on an Excel worksheet

Your age today

Age you'd like to retire

Years Invested

Balance of funds today

Annual Contributions

Expected rate of Inflation

Growth Rate of Cash Flows

Rate of Return on Investments

With the goal of finding the future value, given the above variables

So let's assign some numbers to these variables

Your age today =25

Age you'd like to retire =55

Years Invested 55-25=30

Balance of funds today=0

Annual Contributions=7500

Expected rate of Inflation =4%

Growth Rate of Cash Flows =3.5%

Rate of Return on Investments= 8%

Using the Excel sheet, the professor got a future value of $1,306,055.37. If Excel formula is a big mess of functions and named cells that I haven't bothered to decipher yet, so I wanted to see if I could get the same result as he did by hand.

I thought the answer was

growth $\displaystyle =0.035-0.04=-0.005$

$\displaystyle \frac{7500}{1.08}+\frac{0.995(7500}{1.08^{2}}+...+ \frac{0.995^{29}(7500)}{1.08^{30}}$

To get the present value and then multiply by $\displaystyle 1.08^{30}$ to get the future value.

Which would give

$\displaystyle \frac{7500}{1.08}*\frac{1-(\frac{0.98}{1.08})^{30}}{1-\frac{0.98}{1.08}}*1.08^{30}=713787.94$

That's much lower than what the professor got.

Anyway, I attached the Excel sheet. Maybe someone can decipher it for me. This isn't going to be on any exams or anything, so I doubt the professor will spend the time to go over it