Question

Zoe purchased a house in 1999 for $108,060. In 2003, she sold the house and made a net profit of $580,000. Find the effective annual rate of return on her investment over the 4-year period.

Answer 1

To calculate the effective annual rate of return on Zoe's investment over a 4-year period, we use the compound interest formula to solve for the rate (r), which yields the rate of return she made on her investment.

Step-by-step explanation:

The question involves calculating the effective annual rate of return on Zoe's investment in real estate over a period of four years. To find this rate, we'll use the formula for compound interest to solve for the rate (r). The formula needed is:

A = P(1 + r)n

Where:

• A is the final amount that the investment has grown to after interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (as a decimal).
• n is the number of years the money is invested.

Zoe's investment grew from $108,060 to $108,060 + $580,000 = $688,060 over 4 years. Plugging these values into the formula, we have:

$688,060 = $108,060(1 + r)4

To find r, we solve the equation:

(1 + r)4 = $688,060 / $108,060

1 + r = (($688,060 / $108,060)1/4)

r = (($688,060 / $108,060)1/4) - 1

After calculating this, we get the effective annual rate of return that Zoe made on her investment.