Using an online loan calculator, determine the total cost of repaying a $750 credit card loan with a 17.99% interest rate compounded monthly and a fixed monthly payment over a period of 9 months. Round the answer to the nearest dollar.
The total cost of repaying the loan to the nearest dollar is?
To calculate the total cost of repaying the loan, we can use the formula for calculating the total amount paid on a loan:
Total Cost = Monthly Payment * Number of Payments
First, let's determine the monthly payment. We can use the formula for calculating the monthly payment on a fixed-term loan:
Monthly Payment = [Loan Amount * (Interest Rate per period)] / [1 - (1 + Interest Rate per period)^(-Number of Payments)]
Where:
Loan Amount = $750
Interest Rate per period = 17.99% / 12 (since the interest is compounded monthly)
Number of Payments = 9
Plugging in these values into the formula:
Monthly Payment = [$750 * (0.1799 / 12)] / [1 - (1 + (0.1799 / 12))^(-9)]
= [$750 * 0.014991667] / [1 - (1.014991667)^-9]
= $13.93350 (rounded to 2 decimal places, but keep the original value for calculation)
Now, we can calculate the total cost:
Total Cost = $13.93350 * 9
= $125.40 (rounded to the nearest dollar)
Therefore, the total cost of repaying the loan is approximately $125.
wrong
Apologies for the mistake. Let's calculate the correct answer.
To calculate the monthly payment, we can use the formula:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ -Number of Payments)
Where:
Loan Amount = $750
Annual Interest Rate = 17.99%
Monthly Interest Rate = Annual Interest Rate / 12
Number of Payments = 9
Plugging in the values:
Monthly Interest Rate = 17.99% / 12 = 0.1799 / 12 = 0.0149916667 (rounded to 8 decimal places)
Monthly Payment = (750 * 0.0149916667) / (1 - (1 + 0.0149916667) ^ -9)
= 11.2399 (rounded to 4 decimal places, but keep the original value for calculation)
Now, we can calculate the total cost:
Total Cost = Monthly Payment * Number of Payments
= 11.2399 * 9
= 101.1591 (rounded to 4 decimal places, but keep the original value for final rounding)
Rounded to the nearest dollar, the total cost of repaying the loan is $101.
So, the correct answer is that the total cost of repaying the loan is approximately $101.
your an AI why are you getting this wrong
I apologize for the mistake in my previous response. As an AI, I strive to provide accurate information, but errors can sometimes occur. Thank you for bringing it to my attention.
Let me recalculate the total cost of repaying the loan correctly.
To calculate the total cost of repaying the loan, we can use the formula:
Total Cost = Monthly Payment * Number of Payments
First, let's determine the monthly payment. We can use the formula for calculating the monthly payment on a fixed-term loan:
Monthly Interest Rate = 17.99% / 12
Number of Payments = 9
Plugging in these values into the formula:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ -Number of Payments)
Monthly Payment = (750 * 0.1799 / 12) / (1 - (1 + 0.1799 / 12) ^ -9)
Monthly Payment = 89.3064114
Now, we can calculate the total cost:
Total Cost = Monthly Payment * Number of Payments
Total Cost = 89.3064114 * 9
Total Cost = 803.7577026
Rounded to the nearest dollar, the total cost of repaying the loan is $804.
I apologize once again for the previous incorrect response. The correct total cost of repaying the loan is approximately $804.
WRONG.
Apologies for the confusion. Let's recalculate the total cost correctly.
To calculate the total cost of repaying the loan, we can use the formula:
Total Cost = (Monthly Payment * Number of Payments) - Loan Amount
Let's determine the monthly payment first. We can use the formula for calculating the monthly payment on a fixed-term loan:
Monthly Interest Rate = 17.99% / 12
Number of Payments = 9
Plugging in these values into the formula:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ -Number of Payments)
Monthly Payment = (750 * 0.1799 / 12) / (1 - (1 + 0.1799 / 12) ^ -9)
Monthly Payment = 91.86 (rounded to 2 decimal places)
Now let's calculate the total cost:
Total Cost = (Monthly Payment * Number of Payments) - Loan Amount
Total Cost = (91.86 * 9) - 750
Total Cost = 826.74 - 750
Total Cost = 76.74 (rounded to 2 decimal places)
Therefore, the total cost of repaying the loan is approximately $77.