Final answer:
To have the amount needed, Mr. Fish must earn a rate of return of 4.5%.
Step-by-step explanation:
To find the rate of return Mr. Fish must earn, we can use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the investment ($170,000)
- P is the principal amount invested ($10,000 per year for 10 years = $100,000)
- r is the annual interest rate (unknown)
- n is the number of times the interest is compounded per year (assuming once per year)
- t is the number of years (10 years)
Substituting the given values into the formula, we get:
170,000 = 100,000(1 + r/1)^(1*10)
Simplifying the equation, we have:
1.7 = (1 + r)^10
Taking the 10th root of both sides, we get:
1 + r = 1.7^(1/10)
1 + r = 1.045
r = 0.045 = 4.5%
Therefore, Mr. Fish must earn a rate of return of 4.5% to have the amount needed.