a collector of rare books has a first - edition book worth $262, which he anticipates will grow in value at…

Explanation:

Step1: Identify the compound - growth formula

The formula for compound - growth is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the annual growth rate as a decimal, and $t$ is the number of years.

Step2: Convert the percentage to a decimal

The growth rate $r = 15%=0.15$, the initial value $P = 262$, and the number of years $t = 10$.

Step3: Substitute the values into the formula

$A=262\times(1 + 0.15)^{10}$. First, calculate $(1 + 0.15)^{10}$. Using a calculator, $(1.15)^{10}\approx4.04555773$. Then, multiply by the initial value: $A = 262\times4.04555773\approx1060.936125$.

Step4: Round to the nearest cent

Rounding $1060.936125$ to the nearest cent gives $1060.94$.

Answer:

$1060.94$