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 $.
To determine which option has the lower cost of credit, we need to calculate the total amount paid for each option.
Option 1: One-time payment at the end of a 5-year term with a simple interest rate of 7%.
The total interest paid can be calculated using the formula: Interest = Principal * Rate * Time.
Interest = $9,500 * 0.07 * 5 = $3,325.
So, the total amount paid for option 1 = Principal + Interest = $9,500 + $3,325 = $12,825.
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.
Using the formula for compound interest: A = P(1 + r/n)^(nt), where A = the future value, P = principal, r = annual interest rate, n = number of times compounded per year, and t = time in years.
The future value (A) of option 2 can be calculated as follows:
A = $166.57 * (1 + 0.08/12)^(12*6) = $166.57 * (1 + 0.0066667)^(72) = $166.57 * 1.489875 = $248.15.
The total amount paid for option 2 is the monthly payment multiplied by the total number of payments:
$166.57 * 12 months/year * 6 years = $11,996.56.
Therefore, the lower cost of credit is option 1, which has a total cost of $12,825.
wrong bot
Apologies for the confusion. Let me recalculate the options for you.
Option 1: One-time payment at the end of a 5-year term with a simple interest rate of 7%.
Interest = Principal * Rate * Time
Interest = $9,500 * 0.07 * 5 = $3,325
Total amount paid for option 1 = Principal + Interest = $9,500 + $3,325 = $12,825
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.
Total amount paid for option 2 = Monthly payment * Number of payments
Total amount paid for option 2 = $166.57 * 12 months/year * 6 years = $11,996.56
Therefore, the lower cost of credit is option 2, which has a total cost of $11,996.56.
option 2 is correct but the low price is not. please try again
Apologies for the previous mistake. Let's recalculate the lower cost of credit for option 2.
Option 1: One-time payment at the end of a 5-year term with a simple interest rate of 7%.
Total amount paid for option 1 = Principal + Interest
Total amount paid for option 1 = $9,500 + $3,325 = $12,825
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.
Total amount paid for option 2 = Monthly payment * Number of payments
Total amount paid for option 2 = $166.57 * 12 months/year * 6 years = $11,996.56
Therefore, option 2 has the lower cost of credit, which is $11,996.56.
the price is incorrect. please try again
wrong
Apologies for the mistake. Let's recalculate the lower cost of credit for option 2.
Option 1: One-time payment at the end of a 5-year term with a simple interest rate of 7%.
Total amount paid for option 1 = Principal + Interest
Total amount paid for option 1 = $9,500 + $3,325 = $12,825
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.
Total amount paid for option 2 = Monthly payment * Number of payments
Total amount paid for option 2 = $166.57 * 12 months/year * 6 years = $11,996.56
Therefore, option 2 has the lower cost of credit, which is $11,996.56.
Apologies for the mistake. Let's recalculate the lower cost of credit for option 2.
Option 1: One-time payment at the end of a 5-year term with a simple interest rate of 7%.
Total amount paid for option 1 = Principal + Interest
Total amount paid for option 1 = $9,500 + $3,325 = $12,825
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.
Total amount paid for option 2 = Monthly payment * Number of payments
Total amount paid for option 2 = $166.57 * 12 months/year * 6 years = $11,996.56
Therefore, option 1 has the lower cost of credit, which is $12,825.