Suzanne has purchased a car with a list price of $23,860. She traded in her previous car, which was a Dodge in good condition, and financed the rest of the cost for five years at a rate of 11.62%, compounded monthly. The dealer gave her 85% of the listed trade-in price for her car. She was also responsible for 8.11% sales tax, a $1,695 vehicle registration fee, and a $228 documentation fee. If Suzanne makes a monthly payment of $455.96, which of the following was her original car?

Question

Mathematics

Anastasia Conley

30 December, 01:23

Suzanne has purchased a car with a list price of $23,860. She traded in her previous car, which was a Dodge in good condition, and financed the rest of the cost for five years at a rate of 11.62%, compounded monthly. The dealer gave her 85% of the listed trade-in price for her car. She was also responsible for 8.11% sales tax, a $1,695 vehicle registration fee, and a $228 documentation fee. If Suzanne makes a monthly payment of $455.96, which of the following was her original car?

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Answers (1)

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Clare Summers · Answer 1

The interest is 11.62% compounded monthly. Converting this to an effective rate:

i = (1 + 0.1162/12) ^12 - 1

i = 0.1226

We use this formula to solve the problem:

455.96 = (23860 (1.0811) + 1695 + 228 - C) [0.0811 (1+0.0811) ^3]/[ (1+0.0811) ^3 - 1]

Solving for C

C = 4413.13

The cost of her car was $4,413.13.