Question

You owe $1,853.42 on a credit card with a limit of $3,000.00 at a rate of 15.5% APR. You pay $400.00 the first 2 months and then $200.00 until the bill is paid off. You pay the bill on the due date each month.

1) Complete the table showing the decreasing debt.
2) How much is your last payment?
3) What is the total amount paid by the time you pay off the credit card?
4) What was your debt ratio at the beginning?

Be sure to include in your response:
• All parts of the table are complete and calculations correct
• The answers to the additional questions

Month 1 2 3 4 5 6 7 8 9 10 11
Principal 376.07 380.92
183.54
182.54 179.35 177.90 172.88 198.57
1.64

Interest accrued 23.93
19.08

16.46
17.46 20.65 22.10 27.12 1.43 0.02
Payment (on due date) 400 400 200 200 200 200 200 200 1.66
End-of-month balance 1,477.35 1,096.43 912.89 730.35

550.99
373.09 200.21
1.64
0.00

Answer 1

Monthly rate = APR/12 = 0.155/12 = 0.0129166666667 (≈ 1.2916667% per month).
I round interest to the nearest cent each month, payment is applied first to interest, then to principal. Beginning balance = $1,853.42.

Complete amortization (all amounts in $):

Month | Beg. balance | Interest | Payment | Principal | End balance
1 | 1,853.42 | 23.94 | 400.00 | 376.06 | 1,477.36
2 | 1,477.36 | 19.08 | 400.00 | 380.92 | 1,096.44
3 | 1,096.44 | 14.16 | 200.00 | 185.84 | 910.60
4 | 910.60 | 11.76 | 200.00 | 188.24 | 722.36
5 | 722.36 | 9.33 | 200.00 | 190.67 | 531.69
6 | 531.69 | 6.87 | 200.00 | 193.13 | 338.56
7 | 338.56 | 4.37 | 200.00 | 195.63 | 142.93
8 | 142.93 | 1.85 | 144.78* | 142.93 | 0.00

(*) Month 8 is the final (smaller) payment; you would pay only the balance owed that month ($142.93 + $1.85 interest = $144.78) instead of the full $200.

Answers to the additional questions
2) Last payment = $144.78.
3) Total amount paid = sum of all payments = 400 + 400 + 5·200 + 144.78 = $1,944.78.
- Total interest paid = $1,944.78 − $1,853.42 = $91.36.
4) Debt ratio at the beginning = balance / limit = 1,853.42 / 3,000 = 0.617807… ≈ 61.78%.

If you prefer I can recompute the table using any different rounding convention (e.g., truncating interest instead of rounding).