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Consider a home mortgage of ​$250,000 at a fixed APR of ​4.5% for 30 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.

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sqdancefan

Answer:

  a. payment: $1266.71

  b. total paid: $456, 015.60

  c. fraction to principal: 54.8%; fraction to interest: 45.2%

Step-by-step explanation:

a.

The amortization formula tells you the monthly payment is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

Payment on principal P at annual rate r for t years.

  A = $250,000(0.045/12)/(1 -(1 +0.045/12)^(-12·30)) ≈ $1266.71

The monthly payment is $1266.71.

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b.

360 monthly payments of $1266.71 will have a total value of ...

  360 × $1266.71 = $456,015.60 . . . . total amount paid

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c.

Of course, $250,000 is paid on the principal. That percentage is ...

  $250,000/$456,015.60 × 100% ≈ 54.8% . . . to principal

The remaining fraction is paid for interest:

  100% -54.8% = 45.2% . . . to interest

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