Since a home is probably the single largest and most important purchase the first-time home buyer will make, he must seek out a cheap monthly payment. Start with evaluating monthly income and expenses to ascertain how much he could comfortably manage. He should 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% 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 P is the principal I is the interest rate n is the total number of payments Some numbers in the instance have been rounded for simplicity.
Divide the interest rate (5 percent) by the number of interest periods each year (12) to find an interest rate a period of 0.4 percentage. Substitute 0.004 for in the formulation. Add 1 and 0.004 to return 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 span of the mortgage (n) by multiplying the number of payments each year (12) by the period of the mortgage (30 years) to yield 360. Substitute 360 for n, and raise (1.004) into 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 in 4.2 for a difference of 3.2. Divide 0.017 by 3.2 to return 0.005. M = P (0.017 / / 3.2) = P x 0.005
Multiply $100,000 by 0.005 to afford $500. The principal and interest part of the mortgage is $500 a 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 a month, respectively. Add monthly insurance and property tax to interest and principal for a total monthly payment of $708.33.