Question

you purchase a new house for $240,000 today. if you live in that house for 25 years before selling it, assuming an inflation rate of 5%, compounded continuously, what would be the value of the home when you decide to sell it? round your answer to the nearest cent (hundredth).

Explanation:

Step1: Recall the formula for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $t$ is the time in years, and $e$ is the base of the natural logarithm.
Here, $P = 240000$, $r = 0.05$ (since 5% = 0.05), and $t = 25$.

Step2: Substitute the values into the formula

$A = 240000 \times e^{(0.05 \times 25)}$

First, calculate the exponent: $0.05 \times 25 = 1.25$

Then, calculate $e^{1.25}$. We know that $e^{1.25} \approx 3.4903428543$

Now, multiply by the principal: $240000 \times 3.4903428543 \approx 837682.285032$

Step3: Round to the nearest cent

Rounding $837682.285032$ to the nearest cent gives $837682.29$

Answer:

$\$837682.29$