Question

You are taking out a car loan and will make payments of $400 each month, for a total of 60 monthly payments. You also have $6500 for a down payment. The APR is 10.8% with quarterly compounding. How much does the car cost?

Answer #1

Annual interest rate = 10.80%

Quarterly interest rate = 2.70%

Effective annual rate = (1 + Quarterly interest rate)^4 -
1

Effective annual rate = (1 + 0.0270)^4 - 1

Effective annual rate = 1.11245 - 1

Effective annual rate = 0.11245

Monthly interest rate = (1 + Effective annual rate)^(1/12) -
1

Monthly interest rate = (1 + 0.11245)^(1/12) - 1

Monthly interest rate = 1.00892 - 1

Monthly interest rate = 0.00892 or 0.892%

Monthly payment = $400

Number of payments = 60

Present value of monthly payments = $400/1.00892 +
$400/1.00892^2 + … + $400/1.00892^59 + $400/1.00892^60

Present value of monthly payments = $400 * (1 - (1/1.00892)^60) /
0.00892

Present value of monthly payments = $400 * 46.306808

Present value of monthly payments = $18,522.72

Cost of car = Down payment + Present value of monthly
payments

Cost of car = $6,500 + $18,522.72

Cost of car = $25,022.72

Compare the costs of each car. Calculate the interest to be paid
on both, month payments, total payments and the APR? Car A
??????Car B $24,000 purchase price????$21,5000 purchase price
$3,000 Down payment ????$1,500 Down payment 2.9% Interest rate
?????6.9% Interest rate 4 year loan with monthly payments???6 year
loan with monthly payments

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You make monthly payments on your car loan. It has a quoted APR
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