Question

Laura is currently paying off her four-year car financing. When she purchased her car, it had a list price of $19,858. Laura traded in her previous car, a good-condition 2000 Honda Insight, for 85% of the trade-in value listed below, financing the rest of the cost at 9.5% interest, compounded monthly. She also had to pay 9.27% sales tax, a $988 vehicle registration fee, and a $77 documentation fee. However, because Laura wants to pay off her loan more quickly, she makes a total payment of $550 every month. How much extra is she paying monthly? Round all dollar values to the nearest cent.

Honda Cars in Good Condition
Model/Year
2000
2001
2002
2003
Element
$5,887
$6,080
$6,225
$6,622
Odyssey
$8,450
$8,693
$8,928
$9,224
Insight
$4,384
$4,661
$5,006
$5,440
Accord
$6,356
$6,626
$6,817
$7,114
a.
$73.81
b.
$71.72
c.
$88.24
d.
$77.92

Answer 1

Step 1 — trade‑in credit:
85% of the 2000 Insight value = 0.85 × $4,384.00 = $3,726.40.

Step 2 — sales tax (on the list price):
9.27% of $19,858.00 = 0.0927 × $19,858.00 = $1,840.84.

Step 3 — amount financed (rounding to cents at each step):
Financed principal = list price + sales tax + registration fee + doc fee − trade‑in
= $19,858.00 + $1,840.84 + $988.00 + $77.00 − $3,726.40
= $19,037.44.

Step 4 — required monthly payment for a 4‑year (48‑month) loan at 9.5% APR compounded monthly:
monthly rate i = 0.095/12 ≈ 0.0079166667.
Payment M = P·i / (1 − (1+i)^−48) ≈ $478.28 (rounded to nearest cent).

Step 5 — extra amount Laura pays each month:
Actual payment $550.00 − required payment $478.28 = $71.72.

Answer: b. $71.72.