Question

The price of gold in January 2008 was $846.75 per ounce. In January 2012, the price was $1598 per ounce.
a. What is the change in value?
b. What is the relative change in value?

Answer 1

To calculate the change in value and the relative change in value of gold between January 2008 and January 2012, we can follow these steps:

### a. Change in Value

The change in value is calculated as:

\[
\text{Change in Value} = \text{Price in January 2012} - \text{Price in January 2008}
\]
\[
\text{Change in Value} = 1598 - 846.75 = 751.25
\]

So, the change in value is **$751.25** per ounce.

### b. Relative Change in Value

The relative change in value can be calculated using the formula:

\[
\text{Relative Change} = \frac{\text{Change in Value}}{\text{Original Value}} \times 100\%
\]
where the original value is the price of gold in January 2008.

Substituting our values:

\[
\text{Relative Change} = \frac{751.25}{846.75} \times 100\%
\]

Calculating the relative change:

\[
\text{Relative Change} \approx 0.8852 \times 100\% \approx 88.52\%
\]

So, the relative change in value is approximately **88.52%**.