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 $ ___
wrong
wrong again
please give the correct answer.
Apologies for the previous incorrect responses. Let's calculate the correct answer:
Option 1: One-time payment at the end of a 5-year term with a simple interest rate of 7%.
Total amount paid = Principal + interest
Principal = $9,500
Interest = Principal * Rate * Time = $9,500 * 0.07 * 5 = $3,325
Total amount paid = $9,500 + $3,325 = $12,825
Option 2: Monthly payment of $166.57 with a fixed compound interest rate of 8% compounded monthly over a period of 6 years.
Total amount paid = 72 * monthly payment
Monthly payment = $166.57
Total amount paid = $166.57 * 72 = $11,991.04
Comparing the total amounts paid for each option:
Option 1: $12,825
Option 2: $11,991.04
Therefore, Option 2 has the lower cost of credit.
The lower cost of credit is $11,991.04.
To compare the two payment options, we need to find the total amount paid in each option.
Option 1: One-time payment at the end of 5 years
The simple interest formula is: I = PRT, where I is the interest, P is the principal (loan amount), R is the interest rate, and T is the time (in years).
In this case, P = $9,500, R = 7% (0.07), and T = 5.
The interest for 5 years is: I = 9,500 * 0.07 * 5 = $3,325.
The total amount paid is the loan amount plus the interest: $9,500 + $3,325 = $12,825.
Option 2: Monthly payments over 6 years
The monthly payment is $166.57, and the interest rate is 8% compounded monthly. To find the total amount paid, we need to calculate each monthly payment based on the compound interest formula.
The compound interest formula is: A = P(1 + r/n)^(n*t), where A is the total amount, P is the principal (loan amount), r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.
In this case, P = $9,500, r = 8% (0.08), n = 12 (compounded monthly), and t = 6.
We find the value of A by plugging in the values: A = 9,500(1 + 0.08/12)^(12*6).
Using a financial calculator or spreadsheet, we get A ≈ $13,270.47.
Comparing the total amounts paid for each option:
Option 1: $12,825
Option 2: $13,270.47
Therefore, Option 1 has the lower cost of credit.
The lower cost of credit is $12,825.
Apologies for my mistake. Let's calculate the correct answer:
Option 1: One-time payment at the end of 5 years
The simple interest formula is: I = PRT, where I is the interest, P is the principal (loan amount), R is the interest rate, and T is the time (in years).
In this case, P = $9,500, R = 7% (0.07), and T = 5.
The interest for 5 years is: I = 9,500 * 0.07 * 5 = $3,325.
The total amount paid is the loan amount plus the interest: $9,500 + $3,325 = $12,825.
Option 2: Monthly payments over 6 years
The monthly payment is $166.57, and the interest rate is 8% compounded monthly. To find the total amount paid, we need to calculate each monthly payment based on the compound interest formula.
The compound interest formula is: A = P(1 + r/n)^(n*t), where A is the total amount, P is the principal (loan amount), r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.
In this case, P = $9,500, r = 8% (0.08), n = 12 (compounded monthly), and t = 6.
We find the value of A by plugging in the values: A = 9,500(1 + 0.08/12)^(12*6).
Using a financial calculator or spreadsheet, we get A ≈ $13,270.47.
Comparing the total amounts paid for each option:
Option 1: $12,825
Option 2: $13,270.47
Therefore, Option 1 has the lower cost of credit.
The lower cost of credit is $12,825.
I apologize for the previous incorrect responses. Let's calculate the correct answer:
Option 1: One-time payment at the end of a 5-year term with a simple interest rate of 7%.
Total amount paid = Principal + interest
Principal = $9,500
Interest = Principal * Rate * Time = $9,500 * 0.07 * 5 = $3,325
Total amount paid = $9,500 + $3,325 = $12,825
Option 2: Monthly payment of $166.57 with a fixed compound interest rate of 8% compounded monthly over a period of 6 years.
Total amount paid = 72 * monthly payment
Monthly payment = $166.57
Total amount paid = $166.57 * 72 = $11,995.04
Comparing the total amounts paid for each option:
Option 1: $12,825
Option 2: $11,995.04
Therefore, Option 2 has the lower cost of credit.
The lower cost of credit is $11,995.04.