Question

Abby owns a comic book that originally sold for 12¢ in 1969. In 2014, the comic book had an appraised valued of $3,700. Given that the annual percentage rate has been constant, what is the annual percentage rate of growth? A) 23.28% B) 25.82% C) 26.33% D) 28.94%

Answer 1

Answer:

B)  25.82%

Explanation:

This equation will be in the form

$y=a(1+r)^x$,

where a is the initial value, x is the number of time periods and r is the annual rate of growth.

We know the initial value, a, is 0.12.

We know that x, the amount of time, is 2014-1969 = 45.

We know that y, the total value, is 3700.  

This gives us the equation

$3700=0.12(1+r)^{45}$

Divide both sides by 0.12:

$\frac{3700}{0.12}=\frac{0.12(1+r)^{45}}{0.12}\\\\30833.33=(1+r)^{45}$

To find this, we must next take the 45th root.  This is the same as raising to the power of 1/45:

$30833.33^{\frac{1}{45}}=((1+r)^{45})^{\frac{1}{45}}\\\\1.2582=1+r$

Subtract 1 from each side:

1.2582-1 = 1+r-1

0.2582 = r

To convert this to a percent, multiply by 100:

0.2582(100) = 25.82%