Question

a collector of rare books has a first - edition book worth $262, which he anticipates will grow in value at a rate of 15% per year. how much will this book be worth 10 years from now? if necessary, round your answer to the nearest cent.

Explanation:

Step1: Identify the formula for compound growth

The formula for compound growth is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years.
Here, $P = 262$, $r = 0.15$ (since 15% = 0.15), and $t = 10$.

Step2: Substitute the values into the formula

Substitute $P = 262$, $r = 0.15$, and $t = 10$ into the formula $A = P(1 + r)^t$.
We get $A = 262(1 + 0.15)^{10}$.

Step3: Calculate $(1 + 0.15)^{10}$

First, calculate $1 + 0.15 = 1.15$. Then, calculate $1.15^{10}$. Using a calculator, $1.15^{10}\approx4.045557736$.

Step4: Calculate the final amount

Multiply $262$ by $4.045557736$. So, $A = 262\times4.045557736\approx1059.94$.

Answer:

$\$1059.94$