Monthly payment equals principal times r times one plus r to the n divided by one plus r to the n minus one

Solution

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How It Works

A mortgage amortizes the loan balance through equal monthly payments over a fixed term. Each payment covers that month's interest, with the remainder reducing the principal. Early in the loan, most of the payment goes to interest.

Common terms are 15 and 30 years. A 15-year mortgage has higher monthly payments but significantly less total interest. The calculator also shows total interest paid over the life of the loan.

Example Problem

A $350,000 mortgage at 6.5% for 30 years.

  1. Monthly payment: $2,212.24
  2. Total paid over 30 years: $796,406
  3. Total interest: $446,406

The same loan at 15 years would cost $3,049/month but only $198,843 in total interest — saving $247,563.

Frequently Asked Questions

Should I choose a 15-year or 30-year mortgage?

A 15-year mortgage saves tens of thousands in interest but requires higher monthly payments. On a $300,000 loan at 6%, the 30-year payment is $1,799 vs. $2,532 for 15 years, but total interest drops from $347,515 to $155,683.

What is included in a monthly mortgage payment?

The basic payment covers principal and interest (P&I). Many lenders also escrow property taxes and homeowner's insurance (PITI). PMI may be added if your down payment is less than 20%.

How much mortgage can I afford?

A common guideline is the 28/36 rule: housing costs should not exceed 28% of gross monthly income, and total debt should stay below 36%. On a $6,000/month income, aim for a maximum $1,680 mortgage payment.

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Reference: Brealey, R., Myers, S., & Allen, F. Principles of Corporate Finance. McGraw-Hill Education.