Answer:
$1,504,145.38
Step-by-step explanation:
If the average cost of a home in San Francisco has risen by 15% per year, we can calculate the future value of the house after 3 years by compound interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\\\\A=P\left(1+\dfrac{r}{n}\right)^{nt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$A$ is the future value.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the present value.}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the rate of increase (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times the rate of increase is applied per year.}\\\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}[/tex]
In this case:
Substitute these values into the formula and solve for A:
[tex]A=989000\left(1+\dfrac{0.15}{1}\right)^{1 \times 3}[/tex]
[tex]A=989000\left(1.15\right)^{3}[/tex]
[tex]A=989000\left(1.520875\right)[/tex]
[tex]A=1504145.375[/tex]
Therefore, after three years, the house would be worth $1,504,145.38 (rounded to the nearest cent).
