Answer:
A. $510.75
B. $6,129.00
C. 8.63%
Step-by-step explanation:
You want the monthly payments, total amount paid, and fraction going to interest for the payoff of a $5600 credit card balance at an annual rate of 17% interest.
A. Payments
The monthly payments can be found using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12)) . . . . . P is the principal amount, r is the rate
This formula gives the monthly payment for payoff in 1 year.
A = 5600(0.17/12)/(1 -(1 +0.17/12)^-12) ≈ 510.75
The monthly payment is $510.75.
B. Total paid
You will have made 12 monthly payments of $510.75, for a total of ...
12 × $510.75 = $6,129.00
You will have paid $6,129.00.
C. Fraction to interest
The fraction of your total payoff that goes to interest is ...
(6129 -5600)/6129 = 1 -(5600/6129) ≈ 0.0863 = 8.63%
About 8.63% of your total payment is interest.
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Additional comment
Spreadsheets and calculator apps can be used to find these values. You need to be careful to specify that payments are made at the end of the month.
The amount to interest is slightly more than half the interest that would be due if the interest rate were used to calculate simple interest. Our answer of 8.63% is slightly higher than 17%/2 = 8.5%, so passes the reasonableness check.
