Since a home is likely the single largest and most important purchase the first-time home buyer will make, he should seek an affordable monthly payment. Begin with evaluating monthly income and expenses to determine how much he can comfortably afford. He must also consider additional expenses associated with homeownership, such as homeowner's insurance, property taxes and, in some cases, private mortgage insurance.
Assume principal (amount borrowed) of $100,000, a 5 percent interest rate and a 30-year, fixed-rate mortgage. Assume an annual homeowner's insurance premium or $1,000 and annual property taxes of $1,500. The formula for computing a monthly mortgage payment is M = P [i (1 +i) ^ n] / [(1 +i) ^ n – 1]. M is the monthly principal and interest payment P is the principal i is the interest rate n is the total number of payments Some numbers in the example have been rounded for simplicity.
Divide the interest rate (5 percent) by the number of interest periods per year (12) to get an interest rate per period of 0.4 percent. Substitute 0.004 for i in the formula. Add 1 and 0.004 to yield 1.004. M = P [i (1 + i) ^ n] / [(1 + i) ^ n – 1] = P [0.004 (1 + 0.004) ^ n] / [(1 + 0.004) ^ n – 1] = P (0.004 x 1.004 ^ n) / (1.004 ^ n – 1)
Determine the total number payments over the life of the mortgage (n) by multiplying the number of payments per year (12) by the length of the mortgage (30 years) to yield 360. Substitute 360 for n, and raise (1.004) to the 360th power to yield 4.2. M = P (0.004 x 1.004 ^ n ) / (1.004 ^ n – 1) = P (0.004 x 1.004 ^ 360) / (1.004 ^ 360 – 1) = P (0.004 x 4.2 ) / (4.2 – 1)
Multiply 0.004 by 4.2 to yield 0.017. Subtract 1 from 4.2 for a difference of 3.2. Divide 0.017 by 3.2 to yield 0.005. M = P (0.017 / 3.2) = P x 0.005
Multiply $100,000 by 0.005 to yield $500. The principal and interest portion of the mortgage is $500 per month. M = $100,000 x 0.005 = $500
Divide the homeowner's insurance premium and property tax by 12 to yield $83.33 and $125 per month, respectively. Add monthly insurance and property tax to principal and interest for a total monthly payment of $708.33.
- Electronic spreadsheets and financial calculators have a function for quickly computing monthly payment.
- Your insurance agent can give you an estimate of your annual homeowner's insurance premium.
- Your county tax assessor's office will give you the property tax on an existing home or estimate the tax for new construction.
- Avoid adjustable-rate mortgages in which the interest rate increases after a below-market introductory rate.
- Do not let discretionary new-home expenses--furniture, decorations--wreck your budget.
- calculating image by timur1970 from Fotolia.com