The home that you purchased in 2004 steadily increased in value for the first four years at the annual rate of 5.3%. Then, the home steadily decreased in value for the next three years at the annual rate of 3.4%. If you originally purchased the home for $160,000, what is its value today?
Now, calculate this for each of the years. First, convert the percent to a decimal:
5.3%=.053
3.4%=.034
So, multiply 160,000 by .053 and then add that result to 160,000. Do this four times.
Now, take this end value, and multiply it by .034 and subtract this result from the end value. Do this 3 times. You will have the value for today!
Hope this helps!
value after 4 years of appreciation = 160000(1.053)^4
value of that amount after 3 more years of depreciation = 160000(1.053)^4 (.966)^3
= 177322.91
To find the value of the home today, we need to calculate the increase and decrease in its value over the given years.
Step 1: Calculate the value after the first 4 years of increasing at an annual rate of 5.3%.
To calculate the value after the first year, we multiply the original value by (1 + annual rate).
Value after 1st year = $160,000 * (1 + 0.053) = $160,000 * 1.053 = $168,480.
Following the same process, we can calculate the value after 2, 3, and 4 years:
Value after 2nd year = $168,480 * (1 + 0.053) = $168,480 * 1.053 = $177,164.24.
Value after 3rd year = $177,164.24 * (1 + 0.053) = $177,164.24 * 1.053 = $186,082.90.
Value after 4th year = $186,082.90 * (1 + 0.053) = $186,082.90 * 1.053 = $195,341.02.
Step 2: Calculate the value after the next 3 years of decreasing at an annual rate of 3.4%.
To calculate the value after each year of decrease, we multiply the previous value by (1 - annual rate).
Value after 5th year = $195,341.02 * (1 - 0.034) = $195,341.02 * 0.966 = $188,701.02.
Value after 6th year = $188,701.02 * (1 - 0.034) = $188,701.02 * 0.966 = $182,105.87.
Value after 7th year = $182,105.87 * (1 - 0.034) = $182,105.87 * 0.966 = $176,700.02.
Therefore, the value of the home today is $176,700.02.