Question

Use PMT (r/n) /[1-(1+r/n) ^-n t to determine the regular payment amount, rounded to the nearest dollar. Your credit card has a balance of $1500 and an annual interest rate of 18 %. You decide to pay off the balance over 2 years.
If there are no further purchases charged to the card, how much must you pay each month (round to nearest dollar)?

Answer 1

To calculate the regular monthly payment for paying off your credit card balance of $1500 over 2 years with an annual interest rate of 18%, we can use the formula for the payment on an amortizing loan:

\[
PMT = \frac{(r/n) \cdot P}{1 - (1 + r/n)^{-n \cdot t}}
\]

Where:
- \( P \) is the principal amount (i.e., the balance of the loan, which is $1500).
- \( r \) is the annual interest rate (as a decimal, so 18% becomes 0.18).
- \( n \) is the number of payments per year (since payments are monthly, \( n = 12 \)).
- \( t \) is the number of years (in this case, 2 years).

Now we can plug in the values:

1. Calculate the interest rate per month:
\[
\frac{r}{n} = \frac{0.18}{12} = 0.015
\]

2. Calculate the total number of payments:
\[
n \cdot t = 12 \cdot 2 = 24
\]

Now substitute these values into the PMT formula:

\[
PMT = \frac{(0.015) \cdot 1500}{1 - (1 + 0.015)^{-24}}
\]

Calculating the denominator:

1. Calculate \( (1 + 0.015)^{-24} \):
\[
(1 + 0.015)^{-24} = (1.015)^{-24} \approx 0.644
\]

2. Substitute it back to the equation to find the denominator:
\[
1 - (1.015)^{-24} \approx 1 - 0.644 \approx 0.356
\]

Now, calculate PMT:

\[
PMT = \frac{(0.015) \cdot 1500}{0.356}
\]

Calculating the numerator:

\[
(0.015) \cdot 1500 = 22.5
\]

Finally,

\[
PMT = \frac{22.5}{0.356} \approx 63.19
\]

Rounding to the nearest dollar:

\[
PMT \approx 63
\]

Therefore, the monthly payment amount required to pay off the credit card balance over 2 years is **$63**.