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lapo4ka
26 days ago
9

Olivia is willing to pay $185 a month for four years for a car payment. if the interest rate is 4.9 percent, compounded monthly,

and she has a cash down payment of $2,500, what price car can she afford to purchase?
Business
1 answer:
stepan [3K]26 days ago
4 0
Let x represent the price of the car Olivia can afford.

Down payment = $2,500
The amount left to finance is P = x - 2500.

Total payments should match the monthly payments.
Total payment over 4 years (48 months) is
A = $185*48 = $8,880

The interest rate is r = 4.9% = 0.049.
The compounding frequency is n = 12.
The duration is t = 4 years.
The financed amount is P = $(x - 2500).
Thus,
(x - 2500)(1 + 0.049/12)⁴⁸ = 8880
1.216(x - 2500) = 8880
x - 2500 = 7302.63
x = 9802.63
Thus, Olivia can purchase a car priced at $9,802.63.

Answer: $9,802.63

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