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ID: 1111290 • Letter: A
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a mathxl.com lest: les ll 2 Time Remaining: 00:24:15 Submit Test This Question: 1 pt 15 of 24 (16 complete) This Test: 24 pts possible Kim is shopping for a car. She will finance $7,000 through a lender. The table to the right shows the monthly payments per thousand dollars borrowed at various APRs and terms. Use the table to answer parts (a) through APR,4567 8 (c) below Term, t (in years) 0.06 $23.49 $19.33 $16.57 $14.61 $13.14 0.065 $23.71 $19.57 $16.81 $1485 $13.39 0.075 $24.18 $20.04 $17.29 $15.34 $13.88 (a) One lender offers Kim an APR of 6% for a 6-yr term. What would be the amount of Kim's monthly payment? (b) A competing lender offers an APR of 5.5% but for an 8-yr term. What would be the amount of Kim's monthly payment? Click to select your answers).Explanation / Answer
1. (a) Finance amount = $7,000. APR of 6% for a 6-year term.
Monthly payment per thousand dollars = $16.57
Therefore, monthly payment for an amount of $7,000 = $16.57 x 7
The amount of Kim’s monthly payment = $115.99.
(b) Finance amount = 47,000. APR of 5.5% for an 8-year term.
Monthly payment per thousand dollars = $12.90
Therefore, monthly payment for an amount of $7,000 = $12.90 x 7
The amount of Kim’s monthly payment = $90.30.
(c) (i) For the option described in part (a):
Future value of periodic payment monthly formula:
FV = PMT[(1+i)^nt – 1 / i
(Where PMT is the periodic payment, i. is the interest rate, n is the term, and t is frequency of payment)
FV = $115.99(1+0.06/12)^12x6 / (0.06/12)
FV = 115.99(1.005)^72 - 1 / 0.005
FV = 115.99*(1.432-1)/0.005) = 115.99*(0.432/0.005)
FV = 115.99*86.4
FV = $10,021.54*.
(ii) For the option described in part (b):
FV = $90.3[(1+0.055/12)^12x8 – 1] / (0.055/12)
FV = 90.3(1.0045)^96 - 1/0.0045
FV = 90.3*(1.5388 - 1)/0.0045 = 90.3*(0.5388/0.0045)
FV = 90.3*119.73 = $10,811.60*.
For the option described in part (a), her total payments are $10,021.54.
For the option described in part (b), her total payments are $10,811.60.
1. A. The option in part (a) costs Kim less overall. ($10,021.54).
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