Final answer:
Using the financial calculator method, Gary's monthly loan payment is $444.24. Using the add-on method, Gary's monthly loan payment is $466.67.
Step-by-step explanation:
In order to calculate Gary's monthly loan payment using the financial calculator method, we need to use the formula:
Monthly payment = P * r * (1+r)^n / [(1+r)^n - 1]
Where:
- P is the principal amount ($5,000)
- r is the monthly interest rate (APR / 12)
- n is the number of payments (1 year * 12 months)
So, for Gary's loan:
P = $5,000
r = 12% / 12 = 1%
n = 1 year * 12 months = 12
Plugging these values into the formula gives us:
Monthly payment = $5,000 * 0.01 * (1+0.01)^12 / [(1+0.01)^12 - 1]
Simplifying this expression gives us:
Monthly payment = $5,000 * 0.01 * (1.01^12) / [(1.01^12) - 1]
Calculating this expression gives us:
Monthly payment = $444.24
Therefore, using the financial calculator method, Gary's monthly loan payment is $444.24.
Using the add-on method, we need to calculate the total amount paid over the year and then divide it by 12 to get the monthly payment. The total amount paid over the year would be the principal amount plus the interest, which is:
Total amount paid = principal amount + (principal amount * APR)
For Gary's loan:
Total amount paid = $5,000 + ($5,000 * 0.12)
Simplifying this expression gives us:
Total amount paid = $5,000 + $600 = $5,600
Dividing this total amount by 12 gives us the monthly payment:
Monthly payment = $5,600 / 12 = $466.67
Therefore, using the add-on method, Gary's monthly loan payment is $466.67.