Compare the two payment options for a $9,500 loan to determine which option has the lower cost of credit.

Question

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 $
.
Remaining Attempts : 3

Answer 1

To determine which payment option has the lower cost of credit, we need to calculate the total repayment amount for both options.

Option 1: One-Time Payment at End of Term

Loan Amount: $9,500
Interest Rate: 7% per annum
Term: 5 years

The formula for calculating simple interest is:

\[ \text{Total Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]

Calculating the total interest:

\[ \text{Total Interest} = 9,500 \times 0.07 \times 5 = 3,325 \]

Total amount to be paid back:

\[ \text{Total Repayment} = \text{Principal} + \text{Total Interest} = 9,500 + 3,325 = 12,825 \]

Option 2: Monthly Payments

Loan Amount: $9,500
Interest Rate: 8% per annum (compounded monthly)
Monthly Payment: $166.57
Term: 6 years (72 months)

To find the total repayment amount, we can multiply the monthly payment by the number of months:

\[ \text{Total Repayment} = 166.57 \times 72 = 11,994.04 \]

Summary of Costs

• Option 1 Total Repayment: $12,825
• Option 2 Total Repayment: $11,994.04

Conclusion

Now let's compare the two options:

• Option 1 has a total cost of $12,825.
• Option 2 has a total cost of $11,994.04.

Thus, Option 2 has the lower cost of credit.

The answer is:

Option 2 has the lower cost of credit, which is $11,994.04.