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)
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.