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.
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.