The Mortgage is a particular type of loan that provides for the granting and return of a sum of money against a guarantee represented by real estate. The loan amount can be less than or equal to the selling price of the real estate, while the interest on a mortgage is a tax that is paid on the loan of the money. This is typically depicted as a percentage rate, which means that the interest is a certain fraction of the sum. There are several ways in which a borrower can pay the loan to the lender.
Steps
Method 1 of 3: Examine the Equation to Calculate Mortgage Installments
Step 1. Use the following equation M = P [i (1 + i) ^ n] / [(1 + i) ^ n -1] to calculate the monthly mortgage payment
M is the monthly payment, P is the sum (the loan amount), i is the interest rate, and n the number of installments to be paid.
Step 2. Define the monetary values of M and P
In order to use this formula, these values must be expressed in the same currency.
Step 3. Convert the interest rate i to a decimal fraction
The interest rate must be expressed as a decimal fraction and not a percentage. For example, if the interest rate is 7%, use the value 7/100 or 0.07.
Step 4. Convert the annual interest rate to the monthly rate
The interest rate is usually provided as an annual rate, while the interest on a mortgage is typically compounded on a monthly basis. In this case, divide the annual interest rate by 12 to get the interest rate for the compounding period (monthly average). For example, if the annual interest rate is 7%, divide the decimal fraction 0.07 by 12 to get the monthly interest rate of 0.07/12. In this example, replace i with 0.07 / 12 in the equation from step 1.
Step 5. Define n as the total number of monthly installments needed to pay off the loan
Generally, the loan term is given in years, while the installments are calculated on a monthly basis. In this case, multiply the loan term by 12 to get the number of monthly installments to pay. For example, to calculate the installments of a 20-year loan, substitute 20 x 12 = 240 for the n value in the equation in step 1.
Method 2 of 3: Calculate the Mortgage Installments
Step 1. Determine the monthly mortgage payments of $ 100,000 with an annual interest rate of 5% and a mortgage term of 15 years
Suppose interest is compounded monthly.
Step 2. Calculate the interest rate i
The interest rate as a decimal fraction is 5/100 or 0.05. The monthly interest rate i is then 0.05/12 or about 0.00416667.
Step 3. Calculate the number of installments n
That is 15 x 12 = 180.
Step 4. Calculate the duration (1 + i) ^ n
The duration is given by (1 + 0, 05/12) ^ 180 = approximately 2, 1137.
Step 5. Use P = 100,000 for the mortgage sum
Step 6. Solve 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 amount for this mortgage is $ 790.79.
Method 3 of 3: Review the Impact of the Redemption Term on Interest
Step 1. Suppose the mortgage has a term of 10 years instead of 15
We now have 10 x 12 = 120 rate, so the duration becomes (1 + i) ^ n = (1 + 0, 05/12) ^ 120 = approximately 1.647.
Step 2. Solve 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 amount for this mortgage would then be $ 1,060.66.
Step 3. Compare the total amount of the installments between the 10-year mortgage and the 15-year mortgage, both with 5% interest
The total amount of the installments for 15 years is 180 x 790.79 = $ 142.342.20 and that for the 10-year mortgage is 120 x 1.060.66 = $ 127.279.20 mortgage interest of $ 142.342.20 - $ 127.279.20 = $ 15.063.00.
