$400,000 for 30-years at a fixed APR of 3.87%. The loan payments are monthly and interest is compounded monthly.
what a deal!
Oh - was there a question in there somewhere?
What is the effective annual rate on the loan? (I.e., what is the interest rate once we take into account compounding?)
We don't need the principal nor the time to find the effective annual rate
All we are looking for it the annual rate i, which is equivalent to a rate of .0387/12 per month
that is,
(1+i)^1 = (1+.0387/12)^12
1+i = 1.0393939
i = .03939 or appr 3.939% (note, the decimals only appear to repeat at the beginning, they do not)
check: take 100 for 5 years
at 3.939..%
amount = 100(1.03939...)^5 = 121.315
at 3.87% compouned monthly,
amount = 100(1 + .0387/12)^60 = 121.31
well, how about that?
To calculate the monthly loan payments for a 30-year loan of $400,000 with a fixed APR of 3.87% and monthly compounding interest, you can use the formula for a fixed-rate mortgage payment:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P = Monthly payment
A = Loan amount
r = Monthly interest rate (APR divided by 12 and expressed as a decimal)
n = Total number of monthly payments (30 years * 12 months/year)
First, let's calculate the monthly interest rate:
r = APR / 12 / 100
r = 3.87 / 12 / 100
r = 0.03225
Next, let's calculate the total number of monthly payments:
n = 30 years * 12 months/year
n = 360
Now, we can substitute these values into the formula and solve for P:
P = (0.03225 * 400,000) / (1 - (1 + 0.03225)^(-360))
Calculating this gives us the monthly payment amount.