Zoe purchased a house in 1999 for $196,000. In 2004, she sold the house and made a net profit of $80,000. Find the effective annual rate of return on her investment over the 5-year period. (Round your answer to the nearest hundredth of a percentage point.)

let the rate be i

then ....
196000(1+i)^5 = 276000
(1+i)^5 = 1.408163...
i+i = 1.07085 ..... I took the fifth root of both sides
i = .07085

the effective rate was 7.09%

Thank you!!

Trapezoid has vertices (1,2), (3,2), (1,4), and (3,5). Bounded region is rotated about the y axis. Find the volume using the disk method..

To find the effective annual rate of return on Zoe's investment, we need to determine the growth rate of her initial investment over the 5-year period.

Step 1: Calculate the gain or loss:
Profit = Selling Price - Purchase Price
Profit = $80,000

Step 2: Calculate the percentage gain or loss:
Percentage Gain/Loss = (Profit / Purchase Price) * 100
Percentage Gain/Loss = ($80,000 / $196,000) * 100

Step 3: Calculate the annual growth rate:
Growth Rate = (1 + Percentage Gain/Loss)^ (1 / Number of Years) - 1
Number of Years = 5
Growth Rate = (1 + (80,000 / 196,000))^ (1 / 5) - 1

Finally, we convert the growth rate to a percentage by multiplying by 100 to get the effective annual rate of return.

Step 4: Calculate the effective annual rate of return:
Effective Annual Rate of Return = Growth Rate * 100

Now, let's calculate:

Percentage Gain/Loss = (80,000 / 196,000) * 100 = 40.82%

Growth Rate = (1 + 0.4082)^(1/5) - 1 = 0.0783

Effective Annual Rate of Return = 0.0783 * 100 ≈ 7.83%

Therefore, the effective annual rate of return on Zoe's investment over the 5-year period is approximately 7.83%.