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:
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Calculate the interest rate per month: \[ \frac{r}{n} = \frac{0.18}{12} = 0.015 \]
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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:
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Calculate \( (1 + 0.015)^{-24} \): \[ (1 + 0.015)^{-24} = (1.015)^{-24} \approx 0.644 \]
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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.
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