Example: Loan amortization

Suppose you want to borrow money to buy a house. You are considering a 15-year or a 30-year loan. The lender offers different interest rates, reflecting the differences in risks of shorter-term and longer-term lending. For the 15-year loan, the annual rate is 6.25% (compounded monthly, with 180 equal monthly payments). For the 30-year loan, the annual rate is 6.75% (compounded monthly, with 360 monthly payments). If you borrow $150,000, what would your monthly payments be for each loan?

Answer:

What is the stream of payments necessary to pay off an increasing sum? Use the present value formula to calculate the present value of Pymt_n deposited at the end of n periods discounted at i percent:

PV = Pymt_n * [(1+i)ⁿ - 1] / (1+i)ⁿ * i

Solve for Pymt_n for the 15-year loan:

PV = Pymt_n * [(1+i)ⁿ - 1] / (1+i)ⁿ * i

Pymt₁₈₀ = $150,000 / [(1+.0625/12)¹⁸⁰ - 1] / [(1 + .0625/12)¹⁸⁰ * .0625/12]

Pymt₁₈₀ = $1,286.13

Aren't spreadsheets and calculators grand! Tables would work, but they would have to be big. The monthly payments for the 30-year loan would be $972.90. Click here to view a loan amortization spreadsheet. Many similar programs are also imbedded in realtors' websites - see Dan River Realty's (Pilot Mountain, NC) calculator.

Which loan is better? That depends on what you would do with the difference between $1,286.13 and $972.90 for the first 15 years. Would it be worth having that extra $313.23 for fifteen years and then paying $972.90 for another fifteen years? Your call -- depending perhaps on your personal preference for immediate gratification.

Should you pay off your mortgage? Some homeowners are wondering whether savings in CDs and money market accounts might be better used to reduce or eliminate mortgage payments. There are downsides to paying down, or paying off, your mortgage.

Debating the Pros and Cons Of Paying Off Your Mortgage, Fiscally Fit / Terry Cullen, Wall Street Journal Online - April 10 03.