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