Question

Suppose that you've budgeted $250 per month for a new car, but the salesperson goes into sales mode and talks you into one with a few extra snazzy features. Next thing you know, you have a car payment of $265 per month. Find the actual change and the relative change needed for our car payment budget to accommodate our impulsive decision to go with the fancy car.

Answer 1

To find the actual change, we subtract the original budgeted amount from the new car payment amount:

\[
\text{Actual change} = \text{New car payment} - \text{Budgeted amount}
\]
\[
\text{Actual change} = 265 - 250 = 15
\]

So, the actual change in the car payment is **$15**.

Next, to find the relative change, we use the formula for relative change, which is the actual change divided by the original value (the budgeted amount) expressed as a percentage:

\[
\text{Relative change} = \left( \frac{\text{Actual change}}{\text{Budgeted amount}} \right) \times 100
\]
\[
\text{Relative change} = \left( \frac{15}{250} \right) \times 100
\]
\[
\text{Relative change} = 0.06 \times 100 = 6\%
\]

Therefore, the relative change in the car payment budget is **6%**.

In summary:
- Actual change: **$15**
- Relative change: **6%**