What will a $100,000 house cost 10 years from now if the price appreciation for homes over that period averages 7% compounded​ annually?

Question

I know we are supposed to use the compound interest formula. I would really appreciate it if someone could tell me how to go about this question.

Thank you in advance.

Answer 1

You have to add $7\%$ of the house price at year $t$ to get the house price at year $t+1$.

$$P_{t+1}=P_t+0.07 \cdot P_t=1.07 P_t$$

$$P_{t+2}=P_{t+1}+0.07 \cdot P_{t+1}=1.07 P_{t+1}$$

$$P_{t+2}=P_{t+1}+0.07 \cdot P_{t+1}=1.07 \cdot 1.07 P_t=1.07^2\cdot P_{t}$$

More generally with $t=0$ and $n$ years the formula is

$$P_{n}=1.07^n\cdot P_0$$

$P_0$ ist the current house price: $\$100,000$. With $n=10$ you can calculate the house price in ten years.

Answer 2

You can apply interest formula:

$$A = P(1+\frac{r}{n})^{nt}$$

Then you can plug in what you know:

P = principal value, starting value

r = annual interest rate

n = number of times it's compounded per period (in this case, once per year)

t = number of periods (so 7 years)