a specific type of loan for which the collateral is real property. The loan amount is therefore less than or equal to the sell price of the real estate. The interest on a mortgage loan is a fee that you pay for borrowing money. It’s typically provided as a rate, meaning that the interest is a given fraction of the principle. There are a variety of ways in which a borrower may make mortgage payments to the lender.
Method 1 of 3: Examine the Equation for Mortgage Payments
1Use the following equation M = P[i(1+i)^n]/[(1+i)^n -1] to calculate the monthly payment of a mortgage loan. The monthly payment is M, the principal (amount of the loan) is P, the interest rate is i and the number of payments to make is n.Ad
2Define M and P as monetary values. They must be expressed in units of the same currency in order to use this formula.
3Convert the interest rate i into a decimal fraction. The interest rate must be expressed as a decimal fraction instead of a percentage. For example, if the interest rate is given as 7 percent, use the value 7/100 or 0.07.
4Convert the annual interest rate to the monthly rate. An interest rate is typically given as an annual rate, while the interest on a mortgage loan is typically compounded monthly. In this case, divide the annual interest rate by 12 to get the interest rate for the compounding period (monthly rate). For example, if the annual interest rate is 7 percent, divide the decimal fraction 0.07 by 12 to get the monthly interest rate of 0.07/12. In this example, substitute 0.07/12 for i in the equation given in step 1.
5Define N as the total number of monthly payments required to pay off the loan. Typically, the loan period is given in years while the payments are made monthly. In this case, multiply the term of the loan by 12 to get the number of monthly payments to make. For example, to calculate the payments on a 20 year loan, use 20 x 12 = 240 for the value n in the equation in step 1.
Method 2 of 3: Calculate the Mortgage Payments
1Determine the monthly payments on a $100,000 mortgage with an annual interest rate of 5 percent and a loan term of 15 years. Assume the interest is compounded monthly.
2Calculate the interest rate i. The interest rate as a decimal fraction is 5/100 or 0.05. The monthly interest rate i is therefore 0.05/12 or about 0.00416667.
3Calculate the number of payments n. This is 15 x 12 = 180.
4Calculate the term (1+i)^n. This is given as (1 + 0.05/12)^180 = about 2.1137.
5Use P = 100,000 for the principle of the loan.
6Solve the following equation M = P[i(1+i)^n]/[(1+i)^n -1] to calculate the monthly payment. M = 100,000 x [0.00416667 x 2.1137/2.1137 – 1] = 790.79. The monthly payment on this loan would be $790.79.
Method 3 of 3: Examine the Effect of the Loan Term on Interest
1Assume the mortgage has a 10-year term instead of 15-year term. There are now 10 x 12 = 120 payments, so the term (1+i)^n = (1 + 0.05/12)^120 = about 1.647.
2Solve the following equation M = P[i(1+i)^n]/[(1+i)^n -1] to calculate the monthly payment. M = 100,000 x [0.00416667 x 1.647/1.647 – 1] = 1,060.66. The monthly payment on this loan would therefore be $1,060.66.
3Compare the total payout between the 10-year mortgage and 15-year mortgage, both with 5 percent interest. The total payout for the 15-year loan is 180 x 790.79 = $142,342.20 and the payout for the 10-year loan is 120 x 1,060.66 = 127,279.20. Reducing the term of this loan by 5 years reduces the interest on the loan by $142,342.20 – $127,279.20 = $15,063.00.Ad
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