Final answer:
Barney and Lynn earned approximately a 6.07% annual return on their mutual fund investment over 25 years, historical inflation rates, although below the often expected 10% rate of return for good stock-based mutual funds.
Step-by-step explanation:
To determine the real rate of return on Barney and Lynn's mutual fund investment, we should use the formula for compound interest.
The formula to calculate the final amount (A) is A = P(1 + r/n)^(nt).
Here, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.
In this scenario, they turned a $25,000 investment into $100,000 over 25 years. We can rewrite the compound interest formula to solve for r (the annual interest rate): 100,000 = 25,000(1 + r)^25.
By rearranging the formula and solving for r, we get:
r = (100,000/25,000)^(1/25) - 1
r = (4)^(0.04) - 1
r = 1.0607 - 1
r = 0.0607 or 6.07%
Barney and Lynn earned an average annual return of approximately 6.07%. Given that it is a long-term rate of return, while it does not meet the 10% benchmark often expected of a good stock-based mutual fund, it is still a respectable return, especially considering that it is above the historical average inflation rate.
The information indicates that the average return for the S&P 500 index varied across decades. On average, dividends used to be higher in earlier decades (about 4%) and then decreased to a range of 1% to 2%. This underlines the significance of capital gains, especially in the years when dividends were low.
Regarding whether Barney and Lynn should be bragging about their investment-savvy, it could be argued that while they didn't achieve the 10% target, they still did better than many investors. Remember, most mutual funds don't beat the market average, and having a positive real annual rate of return on their investment is still an achievement.