Question

A gold coin appreciated in value from $200.00 to $475.00 in 6 years. Find the yearly rate of appreciation. Show or explain all work.

Answer 1

Answer:

16%

Step-by-step explanation:

To solve this we are using the standard growth equation:

$y=a(1+b)^x$

Were

$y$ is the final value after $x$ years

$a$ is the initial value

$b$ is the growth factor (yearly rate of appreciation in our case) in decimal form

$x$ is the time in years

We know from our problem that gold coin appreciated in value from $200.00 to $475.00 in 6 years, so $y=475$, $a=200$, and $x=6$.

Let's replace the values in our equation and solve for $b$:

$y=a(1+b)^x$

$475=200(1+b)^6$

$\frac{475}{200} =(1+b)^6$

$2.375=(1+b)^6$

$\sqrt[6]{2.375} =\sqrt[6]{(1+b)^6}$

$1+b=\sqrt[6]{2.375}$

$b=\sqrt[6]{2.375}-1$

$b=0.155$

which rounds to

$b=0.16$

Since our appreciation rate is in decimal form, we need to multiply it by 100% to express it as percentage:

0.16*100% = 16%

We can conclude that the yearly appreciation rate of our gold coin is approximately 16%