You just took out a $200,000 mortgage. you must make equal monthly payments over 30 years, and your interest rate is 6% apr. what is your monthly payment? how much of the first month’s payment is paying interest and how much is paying down the principal balance remaining on the loan?

The monthly payment will be $ 1,555.55 and of that amount, $ 555.55 will correspond to the principal payment and $ 1,000 to the interest payment.

Given that you just took out a $ 200,000 mortgage, and you must make equal monthly payments over 30 years, and your interest rate is 6% APR, to determine what is your monthly payment, and how much of the first month's payment is paying interest and how much is paying down the principal balance remaining on the loan, the following calculation must be performed:

Therefore, the monthly payment will be $ 1,555.55 and of that amount, $ 555.55 will correspond to the principal payment and $ 1,000 to the interest payment.

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  a)  $1199.10

  b)  interest: $1000.00

  c)  principal: $199.10

Step-by-step explanation:

a) The monthly payment can be found using a financial calculator or using the amortization formula:

  A = P(r/12)/(1 -(1+r/12)^(-12t))

for Principal P, annual interest rate r, and time t years.

Filling in the given values and doing the arithmetic yields ...

  A = $200,000(0.06/12)/(1 -(1+0.06/12)^(-12·30)) = 1000/(1 -1.005^-360)

  A ≈ $1199.10

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b) The first month's interest is the monthly interest rate times the initial loan balance:

  = (0.06/12)·(200,000) = 1000.00 . . . . dollars in interest

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c) The first month's payment to principal is the difference between the payment amount and the amount to interest:

  $1199.10 -1000 = $199.10 . . . . . first month's payment on principal

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