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.

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.

GPT-4o mini · Answer

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%