Question

you purchase a home for $125,000. the value of the property increases by 1.9% every year. after ten years, you decide to sell the home. in the meantime, you have made renovations and improvements to the house which increase its sale value by $48,300. how much will you sell the house for, to the nearest hundred dollars?
a. $257,500
b. $209,200
c. $150,900
d. $199,200

please select the best answer from the choices provided

a
b
c
d

Explanation:

Step1: Recall compound growth formula

The formula for compound growth is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual growth rate (in decimal), and $t$ is the time in years. Here, $P = 125000$, $r = 0.019$, and $t = 10$.

Step2: Calculate the value after 10 years due to growth

First, calculate $(1 + 0.019)^{10}$. Let's compute that: $(1.019)^{10}\approx1.207096$. Then, $A = 125000\times1.207096\approx150887$.

Step3: Add the renovation value

Now, add the renovation increase of $48300$: $150887 + 48300 = 199187$.

Step4: Round to nearest hundred

Rounding $199187$ to the nearest hundred gives $199200$.

Answer:

d. $199,200$