Gina bought a $900.00 couch using her credit card. Her credit card had a 20.5% interest rate. What was the difference of her costs of credit if she paid the couch out over 12 months instead of 9 months?
The cost of credit is the amount that a person pays over and above the amount borrowed.
P is the principal, r is the interest rate,
m is the number of monthly payments,
M is the monthly payment
A.
$108.73
B.
$83.59
C.
$78.57
D.
$24.51
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P * r * m = Interest payment over the number of months
900 * .025 * 9 = ?
900 * .025 * 12 = ?
Calculate ? and subtract one from the other.
thankyou
To find the difference in the cost of credit if Gina paid for the couch over 12 months instead of 9 months, we can use the formula for calculating the monthly payment for a loan:
M = (P * r * (1 + r)^m) / ((1 + r)^m - 1)
Where:
M = Monthly payment
P = Principal (amount borrowed)
r = Monthly interest rate (annual interest rate divided by 12)
m = Number of monthly payments
First, let's calculate the monthly interest rate:
r = 20.5% / 12 = 0.0171 (approx.)
Now, let's calculate the monthly payment for 9 months:
m = 9
P = $900.00
r = 0.0171
M9 = (900 * 0.0171 * (1 + 0.0171)^9) / ((1 + 0.0171)^9 - 1)
Using a calculator, we can find that M9 ≈ $108.73 (rounded to the nearest cent).
Next, let's calculate the monthly payment for 12 months:
m = 12
P = $900.00
r = 0.0171
M12 = (900 * 0.0171 * (1 + 0.0171)^12) / ((1 + 0.0171)^12 - 1)
Using a calculator, we can find that M12 ≈ $83.59 (rounded to the nearest cent).
Now, let's calculate the difference in cost of credit:
Difference in cost of credit = (M12 * 12) - (M9 * 9)
Difference in cost of credit = ($83.59 * 12) - ($108.73 * 9)
Using a calculator, we can find that the difference in cost of credit ≈ $78.57 (rounded to the nearest cent).
Therefore, the correct answer is C. $78.57.