To compare the two payment options, we need to calculate the total amount paid in each option and then compare them.
For Option 1:
Simple Interest formula: I = P * r * t
Where:
I = Interest
P = Principal (loan amount)
r = Interest rate per period
t = Number of periods
In this case, P = $9,500, r = 7% = 0.07, and t = 5 years.
I = $9,500 * 0.07 * 5 = $3,325
Total amount paid in Option 1 = P + I = $9,500 + $3,325 = $12,825
For Option 2:
Compound Interest formula: A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal (loan amount)
r = Annual interest rate (convert to a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, P = $9,500, r = 8% = 0.08, n = 12 (compounded monthly), and t = 6 years.
A = $9,500(1 + 0.08/12)^(12*6) = $14,039.65
Total amount paid in Option 2 = A = $14,039.65
Comparing the two options:
Option 1: Total amount paid = $12,825
Option 2: Total amount paid = $14,039.65
The lower cost of credit is Option 1 with a total amount paid of $12,825.
Compare 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.
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