Final answer:
To determine the best loan option, we calculate the total cost of each loan. Great Bank's offer has a total cost of $12,750, Auto Credit Union's offer has a total cost of $12,550, and Quick Loans' offer has a total cost of $12,250. Therefore, Quick Loans is the best option.
Step-by-step explanation:
To determine which loan option is the best, we need to calculate the total cost of each loan. Let's start with Great Bank's offer. They have a no-fee loan with an annual interest rate of 5.5%. Since the loan is for $10,000 and repayable over 5 years, we can calculate the total cost using the formula for compound interest:
Total Cost = Principal + Interest
Total Cost = $10,000 + ($10,000 imes 0.055 imes 5)
Total Cost = $10,000 + $2,750
Total Cost = $12,750
Auto Credit Union offers a loan with an annual interest rate of 4.8% but charges a $150 loan processing fee. So, the total cost can be calculated as:
Total Cost = Principal + Interest + Fee
Total Cost = $10,000 + ($10,000 imes 0.048 imes 5) + $150
Total Cost = $10,000 + $2,400 + $150
Total Cost = $12,550
Lastly, Quick Loans has a no-fee loan with an annual interest rate of 3.9%, but requires your sister to buy a credit life insurance policy for $300. So, the total cost would be:
Total Cost = Principal + Interest + Insurance Cost
Total Cost = $10,000 + ($10,000 imes 0.039 imes 5) + $300
Total Cost = $10,000 + $1,950 + $300
Total Cost = $12,250
Based on the calculations, the loan option with the lowest total cost is Quick Loans, which has a total cost of $12,250.