To calculate the total cost of repaying a $750 credit card loan with a 17.99% annual interest rate compounded monthly over a period of 9 months, we can use the formula for the monthly payment of an installment loan, which is given by:
\[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \]
Where:
- \( M \) is the monthly payment
- \( P \) is the loan principal ($750)
- \( r \) is the monthly interest rate (annual rate / 12)
- \( n \) is the total number of payments (9)
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Calculate the monthly interest rate: \[ r = \frac{17.99%}{12} = \frac{0.1799}{12} \approx 0.01499167 \]
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Substitute the values into the formula: \[ M = 750 \frac{0.01499167(1 + 0.01499167)^9}{(1 + 0.01499167)^9 - 1} \]
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Calculate \((1 + r)^n\): \[ (1 + 0.01499167)^9 \approx 1.149567 \]
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Now substitute this back into the equation: \[ M = 750 \times \frac{0.01499167 \times 1.149567}{1.149567 - 1} \] \[ M \approx 750 \times \frac{0.01721388488}{0.149567} \approx 750 \times 0.115893 \approx 86.92 \]
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The monthly payment \( M \) is approximately $86.92.
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Calculate the total cost of the loan: \[ \text{Total Cost} = M \times n = 86.92 \times 9 \approx 782.28 \]
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Round to the nearest dollar: \[ \text{Total Cost} \approx 782 \]
So, the total cost of repaying the loan to the nearest dollar is $782.
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