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Math Asked by a SnapAndSolve user · about 9 hours ago

For the three-part question that follows, provide your answer to each part in the given workspace. Identify...

For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Jason is buying a home that is worth $275,000. He takes out a 30-year mortgage with a 6% interest rate.
Part A: Determine the monthly payment. Show your work.
Part B: Determine the total 30-year cost. Show your work.
Part C: Determine the interest charge. Show your work.

Answer

Part A: To determine the monthly payment, use the mortgage payment formula:
M = P[r(1+r)^n] / [(1+r)^n – 1]
Where:
M = monthly payment
P = principal loan amount ($275,000)
r = monthly interest rate (annual rate / 12 months = 0.06 / 12 = 0.005)
n = number of payments (30 years * 12 months = 360)

M = 275,000[0.005(1+0.005)^360] / [(1+0.005)^360 – 1]
M ≈ $1,649.18

Part B: Total 30-year cost is the monthly payment multiplied by the number of payments:
Total cost = M * n = $1,649.18 * 360 ≈ $593,704.80

Part C: The interest charge is the total cost minus the principal:
Interest charge = Total cost - Principal = $593,704.80 - $275,000 ≈ $318,704.80

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