You just acquired a mortgage in the amount of $249,000 at 6.75% interest, compounded monthly. Equal payments are to be made at the end of each month for 30 years. How much of the first loan payment is interest? (Assume each month is equal to 1/12 of a year)

good question.

must find the monthly payment.

i = .0675/12 = .005625 (I stored that in my calculator)
n = 12x30 = 360
let the payment be p

p(1 - 1.005625)^-360)/.005625 = 249000
p = 1615.01
first month interest = .005625(on full amount)
= 1400.63

so split-up of first payment:
interest = $1400.63
actual repayment of loan = $214.38

To calculate the amount of the first loan payment that is interest, we need to use the formula for calculating the monthly payment of a mortgage:

M = P * (r * (1+r)^n) / ((1+r)^n - 1)

Where:
M = monthly payment
P = mortgage principal amount
r = monthly interest rate
n = number of monthly payments

First, let's calculate the monthly interest rate. Since the annual interest rate is given as 6.75%, we need to convert it to a monthly rate by dividing it by 12 and converting it to a decimal:

r = 6.75% / 12 / 100 = 0.0675 / 12 = 0.005625

Next, calculate the number of monthly payments over the 30-year period:

n = 30 years * 12 months/year = 360 months

Now we can plug these values into the formula to calculate the monthly payment (M). Once we have the monthly payment, we can determine the amount of the payment that is interest.

M = 249000 * (0.005625 * (1+0.005625)^360) / ((1+0.005625)^360 - 1)

Using a calculator, we find that the monthly payment (M) is approximately $1,618.73.

To find the amount of the first loan payment that is interest, we multiply the outstanding loan balance (the principal amount) by the monthly interest rate:

Interest = P * r

Interest = 249000 * 0.005625 = $1,401.56

Therefore, the amount of the first loan payment that is interest is approximately $1,401.56.