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

16%

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`

`(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%