Georgia purchased a house in 1998 for $220,000. In 2003 she sold the house and made a net profit of $50,000. Find the effective annual rate of return on her investment over the 5-yr period. Please round the answer to the nearest tenth of percent.
let the rate be i
220000(1+i)^5 = 270000
(1+i)^5 = 1.2272727...
take 5th root
1+i = 1.0418..
i = .0418 or appr 4.2% correct to the nearest tenth
To find the effective annual rate of return on an investment over a period of time, we need to use the formula:
Effective annual rate of return = ((Ending value / Beginning value) ^ (1 / number of years)) - 1
In this case, Georgia purchased the house in 1998 for $220,000 and sold it in 2003 with a net profit of $50,000. This means that her ending value in 2003 is $220,000 + $50,000 = $270,000.
The investment period is 5 years (1998-2003), so the number of years is 5.
Plugging the values into the formula:
Effective annual rate of return = (($270,000 / $220,000) ^ (1 / 5)) - 1
Calculating the value within the parentheses:
($270,000 / $220,000) ^ (1 / 5) = 1.1376
Substituting the value back into the formula:
Effective annual rate of return = 1.1376 - 1 = 0.1376
To convert this decimal value to a percentage, we multiply by 100:
0.1376 * 100 = 13.76%
Therefore, the effective annual rate of return on Georgia's investment over the 5-year period is approximately 13.8%.