Compare the two payment options for a $9,500 loan to determine which option has the lower cost of credit.
Option 1: One-time payment to pay off the loan at the end of a 5-year term with a simple interest rate of 7%.
Option 2: Monthly payment of $166.57 with a fixed compound interest rate of 8% compounded monthly; payments made monthly over a period of 6 years.
Find the lower cost of credit. Round the answer to two decimal places as needed.
(1 point)
Option
has the lower cost of credit, which is $
.
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To determine the lower cost of credit, we need to calculate the total amount paid for each payment option.
Option 1:
The simple interest rate of 7% means that each year, the interest is applied to the initial loan amount. So, the total interest paid for the 5-year term is (0.07)(9500) = $665.
Therefore, the total amount paid is $9500 + $665 = $10,165.
Option 2:
The compound interest rate of 8% compounded monthly means that interest is applied to the remaining loan amount each month. To find the monthly payment, we can use the loan payment formula:
P = (PV * R) / (1 - (1 + R)^-N),
where P is the monthly payment, PV is the present value of the loan ($9,500), R is the monthly interest rate (8% divided by 12), and N is the total number of payments (6 years multiplied by 12 months).
Plugging in the values, we get P = (9500 * (0.08/12)) / (1 - (1 + 0.08/12)^(-6*12)), which is approximately $166.57.
The total amount paid over the 6-year term is ($166.57 * 12 * 6) = $11,997.84.
Comparing the total amounts paid, we can see that option 1 has the lower cost of credit, which is $10,165.
wrong
Apologies for the incorrect response. Let's recalculate the cost of credit for each option.
Option 1:
The loan amount is $9,500, and the interest rate is 7%. The loan term is 5 years. To calculate the total cost of credit, we need to find the total interest paid.
Total interest = loan amount * interest rate * loan term = $9,500 * 0.07 * 5 = $3,325.
The total amount paid is the loan amount plus the total interest paid:
Total amount paid = loan amount + total interest paid = $9,500 + $3,325 = $12,825.
Option 2:
The monthly payment is $166.57, and the loan term is 6 years (72 months). To calculate the total cost of credit, we need to find the total payments made.
Total payments = monthly payment * loan term = $166.57 * 72 = $11,995.04.
The total amount paid is the total payments made:
Total amount paid = total payments made = $11,995.04.
Comparing the total amounts paid, we can see that option 1 has the lower cost of credit, which is $12,825.
its option 2 but what is the money part
Apologies for the confusion. You are correct, option 2 has the lower cost of credit. Let's calculate the difference in cost between the two options.
Option 1:
Total amount paid = $12,825
Option 2:
Total amount paid = $11,995.04
To find the difference in cost, subtract the total amount paid for option 2 from the total amount paid for option 1:
Cost difference = Total amount paid for option 1 - Total amount paid for option 2
Cost difference = $12,825 - $11,995.04
Cost difference = $829.96
Therefore, the lower cost of credit for option 2 compared to option 1 is $829.96.