Annuity - Mortgage Payment
Calculate the monthly mortgage payment using the annuity formula.
Problem Scenario
You take a $300,000 mortgage at 6% annual rate (0.5% monthly) for 30 years (360 months).
Given Data
Requirements
- Calculate monthly payment
- Find total interest paid over the life of the loan
Solution
Step 1:
PMT = PV × [r / (1 - (1+r)^-n)].
Step 2:
PMT = 300,000 × [0.005 / (1 - 1.005^-360)].
Step 3:
1.005^-360 = 0.16604. PMT = 300,000 × [0.005 / 0.83396] = 300,000 × 0.005996 = 1,798.65.
Final Answer
Monthly payment ≈ $1,798.65. Total interest = $1,798.65 × 360 - $300,000 = $347,514.
Key Takeaways
- ✓Convert annual rate to monthly before calculating
- ✓Total interest often exceeds the principal on long-term loans
Common Errors to Avoid
- ✗Using annual rate instead of monthly
- ✗Using years instead of months for n
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Common questions about this problem type
Interest = $300,000 × 0.005 = $1,500. Principal = $1,798.65 - $1,500 = $298.65.
Because of compounding over 30 years. Each month you pay interest on the remaining balance, and the balance decreases slowly in early years. Shorter loan terms dramatically reduce total interest paid.