Question

Christina Sanders is concerned about the financing of a home. She saw a small Cape Cod-style house that sells for $90,000. If she

puts 10% down, what will her monthly payment be at (a) 30 years, 5%; (b) 30 years, 5%: (c) 30 years, 6%; and (d) 15 years, 31% ?
What is the total cost of interest over the cost of the loan for each assumption? (Use Table 15.1.)
Note: Round your answers to the nearest cent. Do not round intermediate calculations.
a. 30 years, 5%
b. 30 years, 5 1/2%
c. 30 years, 6%
d. 15 years, 3 7/8%
Monthly payment
Total cost of
interest

Answer 1

Answer: a) 30 years, 5%:

Monthly Payment ≈ $434.65

Total Cost of Interest ≈ $56,075.38

b) 30 years, 5 1/2%:

Monthly Payment ≈ $458.63

Total Cost of Interest ≈ $70,308.97

c) 30 years, 6%:

Monthly Payment ≈ $485.24

Total Cost of Interest ≈ $84,086.35

d) 15 years, 3 7/8%:

Monthly Payment ≈ $591.24

Total Cost of Interest ≈ $23,223.07

Step-by-step explanation: To calculate the monthly payment and the total cost of interest for each scenario, we can use the formula for calculating mortgage payments:

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

Total Cost of Interest = (Monthly Payment * n) - P

Where:

P = Loan amount (purchase price - down payment)

r = Monthly interest rate (annual interest rate / 12)

n = Total number of monthly payments

Let's calculate the values for each scenario:

a) 30 years, 5%

P = $90,000 - (10% * $90,000) = $81,000

r = 5% / 100 / 12 = 0.004167 (approx.)

n = 30 * 12 = 360

Monthly Payment = $81,000 * 0.004167 * (1 + 0.004167)^360 / ((1 + 0.004167)^360 - 1)

Monthly Payment ≈ $434.65

Total Cost of Interest = ($434.65 * 360) - $81,000

Total Cost of Interest ≈ $56,075.38

b) 30 years, 5 1/2%

P = $90,000 - (10% * $90,000) = $81,000

r = 5.5% / 100 / 12 = 0.004583 (approx.)

n = 30 * 12 = 360

Monthly Payment = $81,000 * 0.004583 * (1 + 0.004583)^360 / ((1 + 0.004583)^360 - 1)

Monthly Payment ≈ $458.63

Total Cost of Interest = ($458.63 * 360) - $81,000

Total Cost of Interest ≈ $70,308.97

c) 30 years, 6%

P = $90,000 - (10% * $90,000) = $81,000

r = 6% / 100 / 12 = 0.005 (approx.)

n = 30 * 12 = 360

Monthly Payment = $81,000 * 0.005 * (1 + 0.005)^360 / ((1 + 0.005)^360 - 1)

Monthly Payment ≈ $485.24

Total Cost of Interest = ($485.24 * 360) - $81,000

Total Cost of Interest ≈ $84,086.35

d) 15 years, 3 7/8%

P = $90,000 - (10% * $90,000) = $81,000

r = 3.875% / 100 / 12 = 0.003229 (approx.)

n = 15 * 12 = 180

Monthly Payment = $81,000 * 0.003229 * (1 + 0.003229)^180 / ((1 + 0.003229)^180 - 1)

Monthly Payment ≈ $591.24

Total Cost of Interest = ($591.24 * 180) - $81,000

Total Cost of Interest ≈ $23,223.07

To summarize:

a) 30 years, 5%:

Monthly Payment ≈ $434.65

Total Cost of Interest ≈ $56,075.38

b) 30 years, 5 1/2%:

Monthly Payment ≈ $458.63

Total Cost of Interest ≈ $70,308.97

c) 30 years, 6%:

Monthly Payment ≈ $485.24

Total Cost of Interest ≈ $84,086.35

d) 15 years, 3 7/8%:

Monthly Payment ≈ $591.24

Total Cost of Interest ≈ $23,223.07