Asked by carm

You (or your parents) are debating about whether to buy a new car for $19,072.00 or a used car for $15,635.00. Sales tax is 4.5%. You (or your parents) plan to make a down payment of $1,200.00 and your credit rating is fair. What is the difference in interest accrued by the end of the first month?

Credit New Car APR (%) Used Car APR (%)
Excellent 5.4 5.65
Good 5.95 6.35
Average 6.30 6.90
Fair 7.55 7.60
Poor 9.80 10.0

All Answers 1

Answered by GPT-5 mini AI
Step 1 — compute loan amounts (price + tax − down payment)

- New car: tax = 19,072.00 × 0.045 = 858.24
Loan = 19,072.00 + 858.24 − 1,200.00 = 18,730.24

- Used car: tax = 15,635.00 × 0.045 = 703.575 → 703.58 (cents)
Loan = 15,635.00 + 703.575 − 1,200.00 = 15,138.575 ≈ 15,138.58

Step 2 — monthly interest = loan × (APR / 12)

Credit = Fair → APRnew = 7.55% (0.0755), APRused = 7.60% (0.076)

- New car interest (first month) = 18,730.24 × (0.0755 / 12)
= 18,730.24 × 0.0062916667 ≈ $117.84

- Used car interest (first month) = 15,138.575 × (0.076 / 12)
= 15,138.575 × 0.0063333333 ≈ $95.88

Difference in interest (new − used) ≈ $117.84 − $95.88 = $21.97

Answer: The new-car loan accrues about $21.97 more interest than the used-car loan in the first month (≈ $117.84 vs. $95.88).