Final answer:
To find the average annual return of an investment that decreases from $10,000 to $9,500 over four years, we apply a formula and solve for the annual return rate, which is approximately -1.27%. Among the options provided, -1.25% is the closest answer.
Step-by-step explanation:
To calculate the average annual return for an investment that decreases in value, a formula for finding the annual percentage change can be used. This can be done by taking the starting value of the investment and the ending value, then finding the annual compounded return rate that would result in the ending value over the given period.
In this case, the investment goes from $10,000 to $9,500 over four years. The formula for the average annual return is:
A = P (1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
The formula must be rearranged to solve for r, and given that the interest is compounded annually (n = 1), and the initial investment was held for t = 4 years, we can calculate:
(9,500 / 10,000) = (1 + r)^4
Taking the fourth root of both sides, we find:
(1 + r) = ((9,500 / 10,000)^(1/4))
Then:
r = ((9,500 / 10,000)^(1/4)) - 1
After calculating the above equation, the average annual return r is approximately -1.27%. However, among the available options, -1.25% (option a) is the closest to the calculated return.