Question

CAN SOMEONE PLZ HELP ME?!?!?!

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

the answer is B. $71.72

Answer 2

List price of new car = $19,858
Value of old car = $4,384
Amount traded in with old car = 85% of $4,384 = 0.85 x $4,384 = $3,726.40
Amount owed after trade in = $19,858 - $3,726.40 = $16,131.60
Value of sales tax = 9.27% of $19,858 = 0.0927 x $19,858 = $1,840.84
Total amount owed after purchase of car = $16,131.60 + $1,840.84 + $988 + $77 = $19,037.44

Since she is liduidating the dept by a series of monthly payments, this amounts to an annuity liqidation with present value (PV) = $19,037.44; rate (r) = 9.5% = 0.095; n = four years.

The present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt) / (r/t); where P is the periodic payment, i.e. monthly payment; and t is the number of payments in one year.
19,037.44 = P(1 - (1 + 0.095/12)^-(4 x 12)) / (0.095 / 12)
(0.095 x 19,037.44) / 12 = P(1 - (1 + 0.095/12)^-48)
150.7131 = P(1 - 0.6849) = 0.3151P
P = 150.7131 / 0.3151 = $478.28

Thus, she is supposed to be making a monthly payment of $478.28.
Since she pays $550 monthly, therefore, she pays $550 - $478.28 = $71.72 extra every month.