Question: A cloud storage engineer purchased a new car for $30,990. Complete the table below to determine the cost of owning the car for the first year of ownership. Assume an average fuel efficiency of 35 miles per gallon and a 4-year loan at an annual interest rate of 3.75% on the purchase price less the down payment. (Round your answers to the nearest cent.)
License and registration
0.75% of purchase price
$ 232.43
Sales tax
6.25% of purchase price
$ 1936.88
Down payment
15% of purchase price
$ 4648.5
Depreciation
21% of purchase price
$ 6507.9
Fuel cost driving
14,000 miles
Average cost of gasoline:
$2.71 per gallon
$
Loan payments for 1 year
12 times monthly payment
$
Insurance
$724
$ 724
Maintenance
$358
$ 358
Total
$
1. **State the problem:** Calculate the cost of owning the car for the first year including license, sales tax, down payment, depreciation, fuel cost, loan payments, insurance, and maintenance.
2. **Given data:**
- Purchase price $P = 30990$
- License and registration = 0.75% of $P$
- Sales tax = 6.25% of $P$
- Down payment = 15% of $P$
- Depreciation = 21% of $P$
- Fuel efficiency = 35 miles/gallon
- Miles driven = 14000 miles
- Gasoline cost = $2.71$ per gallon
- Loan term = 4 years
- Annual interest rate = 3.75%
- Insurance = $724$
- Maintenance = $358$
3. **Calculate license and registration:**
$$\text{License} = 0.0075 \times 30990 = 232.425 \approx 232.43$$
4. **Calculate sales tax:**
$$\text{Sales tax} = 0.0625 \times 30990 = 1936.875 \approx 1936.88$$
5. **Calculate down payment:**
$$\text{Down payment} = 0.15 \times 30990 = 4648.5$$
6. **Calculate depreciation:**
$$\text{Depreciation} = 0.21 \times 30990 = 6507.9$$
7. **Calculate fuel cost:**
- Gallons used:
$$\frac{14000}{35} = 400 \text{ gallons}$$
- Fuel cost:
$$400 \times 2.71 = 1084.00$$
8. **Calculate loan payments:**
- Loan amount = purchase price - down payment
$$30990 - 4648.5 = 26341.5$$
- Monthly interest rate:
$$\frac{3.75}{100 \times 12} = 0.003125$$
- Number of payments:
$$4 \times 12 = 48$$
- Monthly payment formula:
$$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$
where $P=26341.5$, $r=0.003125$, $n=48$
Calculate:
$$ (1+0.003125)^{48} = 1.161472$$
$$ M = 26341.5 \times \frac{0.003125 \times 1.161472}{1.161472 - 1} = 26341.5 \times \frac{0.0036296}{0.161472} = 26341.5 \times 0.02249 = 592.15$$
- Annual loan payment:
$$592.15 \times 12 = 7105.80$$
9. **Insurance and maintenance:**
Given as $724$ and $358$ respectively.
10. **Calculate total cost:**
Sum all costs except down payment (since it is upfront, not annual cost):
$$232.43 + 1936.88 + 6507.9 + 1084 + 7105.80 + 724 + 358 = 17949.01$$
**Final table values:**
- License and registration: $232.43$
- Sales tax: $1936.88$
- Down payment: $4648.5$
- Depreciation: $6507.9$
- Fuel cost driving 14,000 miles: $1084.00$
- Loan payments for 1 year: $7105.80$
- Insurance: $724$
- Maintenance: $358$
- Total (excluding down payment): $17949.01$