Mr. Fish wants to build a house in 10 years. He estimates that the total cost will be $170,000. If he can put aside $10,000 at the end of each year, what rate of return must he …

Question

asked Jul 11, 2024 133k views

1 Answer

Kannan G · Answer 1 · 2024-07-18T01:51:55+0000

To have the amount needed, Mr. Fish must earn a rate of return of 4.5%.

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.