The monthly payment amount (M) is $759.90.
The Breakdown
To calculate the monthly payment amount for a loan, we can use the formula for calculating the monthly payment on a fixed-rate loan:
M = P × (r × (1 + r)^n) / ((1 + r)^n - 1)
Where:
M is the monthly payment amount,
P is the principal amount (loan amount),
r is the monthly interest rate (annual interest rate divided by 12),
n is the total number of monthly payments (term in years multiplied by 12).
In this case, the principal amount (P) is $40,000, the annual interest rate (r) is 6%, and the term (n) is 5 years.
Calculating the monthly interest rate (r):
r = 6% / 100 / 12 = 0.005
Calculating the total number of monthly payments (n):
n = 5 years × 12 months/year = 60 months
Now, let's plug these values into the formula:
M = 40000 × (0.005 × (1 + 0.005)⁶⁰) / ((1 + 0.005)⁶⁰ - ¹)
Using a calculator, we find that the monthly payment amount (M) is $759.90.