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.
If the total of all payments for the original budgeted amount is $12,000, how much extra would you end up paying for the snazzy features?
If the total of all payments for the original budgeted amount is $12,000, how much extra would you end up paying for the snazzy features?
Answers
GPT-4o mini
To calculate the actual change in the car payment and the relative change, we can start by finding the difference between the new payment and the original budgeted amount.
### Actual Change:
1. **Original Payment (Budgeted):** $250
2. **New Payment:** $265
Now, we calculate the actual change:
\[
\text{Actual Change} = \text{New Payment} - \text{Original Payment} = 265 - 250 = 15
\]
So the actual change is **$15**.
### Relative Change:
To find the relative change, we use the formula:
\[
\text{Relative Change} = \frac{\text{Actual Change}}{\text{Original Payment}} \times 100
\]
Substituting in the values:
\[
\text{Relative Change} = \frac{15}{250} \times 100 = 6\%
\]
So the relative change is **6%**.
### Total Payments:
Now to find out how much extra you would end up paying for the snazzy features over the total period of the car payments.
1. The total payments for the original budgeted amount:
- Original Payment: $250 per month for a year (12 months)
\[
\text{Total for Original Payment} = 250 \times 12 = 3000
\]
2. The total payments for the new payment:
- New Payment: $265 per month for a year (12 months)
\[
\text{Total for New Payment} = 265 \times 12 = 3180
\]
3. The difference in total payments gives us the extra amount spent due to the snazzy features:
\[
\text{Extra Paid} = \text{Total for New Payment} - \text{Total for Original Payment} = 3180 - 3000 = 180
\]
Thus, you would end up paying an extra **$180** for the snazzy features over the course of the year.
### Summary:
- Actual Change: **$15**
- Relative Change: **6%**
- Extra Payment for Snazzy Features: **$180**
### Actual Change:
1. **Original Payment (Budgeted):** $250
2. **New Payment:** $265
Now, we calculate the actual change:
\[
\text{Actual Change} = \text{New Payment} - \text{Original Payment} = 265 - 250 = 15
\]
So the actual change is **$15**.
### Relative Change:
To find the relative change, we use the formula:
\[
\text{Relative Change} = \frac{\text{Actual Change}}{\text{Original Payment}} \times 100
\]
Substituting in the values:
\[
\text{Relative Change} = \frac{15}{250} \times 100 = 6\%
\]
So the relative change is **6%**.
### Total Payments:
Now to find out how much extra you would end up paying for the snazzy features over the total period of the car payments.
1. The total payments for the original budgeted amount:
- Original Payment: $250 per month for a year (12 months)
\[
\text{Total for Original Payment} = 250 \times 12 = 3000
\]
2. The total payments for the new payment:
- New Payment: $265 per month for a year (12 months)
\[
\text{Total for New Payment} = 265 \times 12 = 3180
\]
3. The difference in total payments gives us the extra amount spent due to the snazzy features:
\[
\text{Extra Paid} = \text{Total for New Payment} - \text{Total for Original Payment} = 3180 - 3000 = 180
\]
Thus, you would end up paying an extra **$180** for the snazzy features over the course of the year.
### Summary:
- Actual Change: **$15**
- Relative Change: **6%**
- Extra Payment for Snazzy Features: **$180**