# Vanguard S&P 500 Mutual Fund has an average of 10% annual gain for any given period of 20 consecutive years?

Is it true that Vanguard S&P 500 Mutual Fund has an average of 10% annual gain for any given period of 20 consecutive years since the great depression?

If my math is correct, than if I were to invest equal installments every year for 20 years with them, then my total gain would be (1-(1.1)^(21))/(1-1.1)/20=3.2 times the amount of money invested over that 20 years.

Are both of these statements correct?

Take a peek at the discussion at Should I continue to invest in an S&P 500 index fund?, in which I offer a look at the returns over shorter periods. The 20 yr returns are as follows

The total returns in the middle col, and CAGR last. These are the returns for all 20 year periods from 1900-2014. It shows an average of 11%, and a minimum 3%. In other words, of 96 time periods, 51 were less than 10%, 45 were greater, and the average, 11.2%.

MoneyChimp offers S&P data easily copied into a spreadsheet. And you can manipulate to analyze as you wish.

The nature of returns is closer to a bell curve. You can't make that final assumption that you suggested. The disparity between getting less than 3X your money vs over 20X over the bad/good 20 year periods is what makes for difficulty planning strategies.

On a personal note - I am semi-retired. 53 yrs old. How different could I spend if I knew with certainty whether the next 40 years would return 3% vs 11%? (min, vs ave, I won't even fantasize over 15%+)

• Thanks for the answer and links. I am not an experienced investor, I am just a physics graduate student, but I am interested in learning more on how to invest from age less than 30. I was told that a mutual fund with Vanguard was a good option, but I wanted to read more about. Thanks. – linuxfreebird Oct 4 '15 at 17:36
• Glad to help. Choosing between their mutual fund and ETF is another discussion, VFINX has a .17% annual expense vs VOO .05% but a trade fee. Either way, take these off the top with respect to my numbers. – JTP - Apologise to Monica Oct 4 '15 at 19:17

R = I ^ P (RIP, rest in peace)

R is total return. 2 means 'double your money'

I is (the interest rate /100) +1. 10% would be 1.1

P = number of periods in which the interest is paid

1.1 ^ 20 = (approx.) 6.73

20 years of 10% interest rate per year is more than 3.2. However you do needneed to cut 6.73 in half since you are contributing in installments and not one big lump sum at the start. So figure 3.36 as your teturn. (if you contribute the same amount each of the 20 years)