Answer:
Step-by-step explanation:
You want the number of months and the total amount paid when you pay off a credit card debt of $1367.90 with 9.5% APR at the rate of $400 each month.
Amortization
The amount of the payment that goes to interest each month is the monthly rate (9.5%/12) multiplied by the remaining balance. The first month's interest is ...
$1367.90 × 0.095/12 = $10.8292 ≈ $10.83 . . . . rounded to cents
Then the balance is reduced by ...
$400 -10.83 = $389.17
so it becomes ...
$1367.90 -389.17 = $978.73 . . . . . balance after first payment
These calculations are repeated for subsequent payments. It is convenient to let a spreadsheet do them. (It can round the interest for you.) The results are shown in the attachment.
Final payment
The negative balance for month 4 reflects the overpayment that a payment of $400 would be. The actual month 4 payment is the previous balance ($191.12) together with the interest due on that ($1.51), so is $192.63.
Total repaid
The total repaid is the sum of interest charges ($24.73) and the initial balance ($1367.90). That is, you paid off the initial balance and the interest due.
You repaid a total of $1392.63 in 4 months.
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Additional comment
The steps for computing the total repaid are ...
- compute the interest due on the remaining balance
- add that to the principal due, and subtract the payment amount to get the new principal due.
- repeat until the new balance is negative, signifying the amount of overpayment.
- Add the interest amounts to the initial balance to find the total repaid.
Note, there are formulas for the payoff time and the total repaid. However, they do not take into account rounding of intermediate values, and they presume the last payment is made partway through the month. In short, it only gives an approximation of the amount repaid.
By listing actual amounts, rounded to cents, the actual amount repaid can be figured with no error. A spreadsheet is very helpful for that.
