ompare the two payment options for a $9,500 loan to determine which option has the lower cost of credit.%0D%0A%0D%0AOption 1: One-time payment to pay off the loan at the end of a 5-year term with a simple interest rate of 7%.%0D%0AOption 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.%0D%0AFind the lower cost of credit. Round the answer to two decimal places as needed.(1 point)

Answer 1

To compare the two payment options, we need to calculate the total cost of credit for each option.

Option 1:
The simple interest formula is: Interest = Principal * Rate * Time
In this case, Principal = $9,500, Rate = 7%, and Time = 5 years.

Interest = $9,500 * 0.07 * 5 = $3,325

The total cost of credit for Option 1 is $3,325.

Option 2:
To calculate the monthly payment for a loan with compound interest, we can use the loan payment formula: Payment = Principal * (Rate*(1+Rate)^Time) / ((1+Rate)^Time - 1)
In this case, Principal = $9,500, Rate = 8%, Time = 6 years.

Payment = $9,500 * (0.08*(1+0.08)^6) / ((1+0.08)^6 - 1) = $166.57

Since payments are made monthly over a period of 6 years, the total cost of credit can be calculated by multiplying the monthly payment by the number of payments: Total cost of credit = Payment * Number of Payments
Number of payments = 6 years * 12 months/year = 72 months

Total cost of credit = $166.57 * 72 = $11,996.64

The total cost of credit for Option 2 is $11,996.64.

Comparing the two options, we can see that Option 1 has a lower cost of credit ($3,325) compared to Option 2 ($11,996.64). Therefore, Option 1 is the lower cost option.