what is the formula used and the values used for each variable to calculate the monthly payment of $804.45 and the amount of the loan is $50000.
To calculate the monthly payment, we need to use the formula for an amortizing loan. The formula is as follows:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate
n = Number of monthly payments
To calculate the monthly payment of $804.45, we can rearrange the formula and solve for r. Let's substitute the given values into the formula:
M = $804.45
P = $50,000
n = Number of payments (unknown for now)
r = Monthly interest rate (unknown for now)
1. First, let's determine the number of monthly payments (n). If you know the term of the loan in years (T), you can multiply it by 12 to get the number of payments. For example, a 5-year loan would have n = 5 * 12 = 60 payments.
2. Now, substitute the known values into the formula:
$804.45 = $50,000 * (r * (1 + r)^n) / ((1 + r)^n - 1)
3. Rearrange the formula and isolate (1 + r)^n:
((1 + r)^n - 1) = (r * (1 + r)^n) / $50,000
4. Solve for (1 + r)^n:
((1 + r)^n - 1) / r = (1 + r)^n / $50,000
5. Apply trial and error or an iterative method to solve for r (monthly interest rate) that satisfies the equation.
Note: The specific values for n and r will vary depending on the term of the loan and the interest rate. In this case, you need to iterate or use numerical methods to calculate the interest rate (r) that would result in a monthly payment of $804.45 for a $50,000 loan.