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Lindsay needs to purchase a car. The car she is planning on purchasing costs $8,000 and she has $2,000 that she will be using as a down payment. She is offered credit terms of 3% APR for a term of 3 years. Please calculate the following: 1) The total amount of interest she will pay over the 3 year period (in dollars) 2) The actual cost of the car after financing is added in (in dollars) 3) The monthly payment she will owe (in dollars)

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nobillionaireNobley
Balance outstanding = $8,000 - $2,000 = $6,000
Let the monthly payment be $P, then
PV = P(1 - (1 + r)^-n)/r); where PV is the amount owing = $6,000; r is the rate = 3%/12 = 0.25% = 0.0025; n is the number of periods = 3 x 12 = 36 months.

6,000 = P(1 - (1 + 0.0025)^-36)/0.0025)
P = 6,000(0.0025)/(1 - (1.0025)^-36) = $174.49

Thus the monthly payment she will owe = $174.49

The actual cost of the car after financing is added in = $2,000 + $174.49 x 36 = $8,281.54

The total amount of interest she will pay = $8,281.54 - $8,000 = $281.54

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