Question

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?

Answer 1

Answer:

  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