Final answer:
Bob's annual return on his investment can be calculated using the future value of an annuity formula. Since the equation for the rate is nonlinear, iteration or a financial calculator is needed to find the exact annual return rate. Historical data provides an average of 7% as a potential reference point.
Step-by-step explanation:
To find Bob's annual return on his investment, we need to use the formula for the future value of an annuity because he has been making regular investments at the end of each year. The formula for the future value of an annuity is:
FV = Pmt * (((1 + r)^n - 1) / r)
Where:
FV = future value of the investment
Pmt = annual payment (investment)
r = annual interest rate (return)
n = number of payments
Let's calculate his annual return:
First, we know that Bob has made an annual investment (Pmt) of $2,000.
His account is currently worth $25,690, which is the future value (FV) of his investments.
He has been investing for 9 years, so n is 9.
To find the annual return (r), we need to solve the annuity formula for r. This requires iteration or a financial calculator because the equation is nonlinear.
Without exact calculations provided, as this isn’t a calculation service, the actual return would be such that if you plug in r in the annuity formula with the provided values of Pmt, n, and FV, the equation should hold true.
Historical data suggests that a well-diversified stock portfolio can yield an average of 7% real annual rate of return, which could be used as an initial estimate to iterate around.