![]() ![]() The C# code for calculating the mortgage takes all the input fields from the NumericUpDown controls and the ThousandTextBox controls and plugs them into the mortgage formula. The ThousandsTextBox also has a property CurrentValue that allows you to translate between the double and string value inside the text box.įigure 2 - UML Class Diagram for the Mortgage Calculator The Mortgage Calculator consists of just two classes: a Windows Form for accepting input and for doing the calculation, and a ThousandsTextBox that overrides the TextBox control class in order to allow the user to type in numbers and handle the comma separator for the thousands place. (This is not including the yearly property tax and the home owner's insurance). In other words, you would need to pay $599.56 monthly for 30 years to pay off a $100,000 loan at 6%. Now solve for x to get our monthly payment. Let's plug this formula in for our $100,000 loan at 6% over 30 years (360 months)ġ00,000 (1 +. Substituting the formula for the total mortgage into the equation, The final formula for a mortgage (known as the amortization equation) is shown below: Total Mortgage = (Loan Value) * (1 + r/12) p The actual value of the total mortgage is the initial loan value compounded over the period of time the loan is paid: So plugging our geometric formula for mortgages into the geometric progression equation gives us: Taking the two equations for f(n+1) and using substitution: + z n) = 1 + z f(n)Īlso (more obviously), the next sum in the progression equals the previous sum plus the next highest factor The definition of a geometric progression can also be viewed by saying that the following: The next sum in the geometric progression can be defined by the taking the previous sum, multiplying all parts of the series by the factor and then adding 1 to it.Īnother words: f(n) = 1 + z + z 2 + z 3 +. Let's show that the geometric formula works: If you have any doubts about this formula. This compound interest formula is a geometric progression and geometric progressions can be reduced to the formula:ġ + z + z 2 + z 3 +. ![]() So the sum of the payments after p months The following month you will pay (x + x * r/12), and in the third month, x + (2x + x* r/12) *r/12 = x ( 1 + r/12) 2. The total worth of the loan is compounded monthly, and the monthly payment is determined by dividing the entire compounded cost of the loan by the total number of months. With this in mind, how does a bank come up with your payment per month? For a 30 year mortgage at 6% you pay more than two times the cost. You actually wind up paying a lot more than $100,000. ![]() Plus, you need to pay property taxes, home owner's insurance, points, and other costs that pop out of the woodwork (so to speak). 5% compounded over the length of the loan. Therefore, you are paying an interest each month of 6%/12 or about. The yearly interest rate is applied fractionally per month and compounded over the life of the mortgage. Say you are buying a $100,000 home at a fixed interest rate of 6% for a 30 year loan. Many first time home buyers are stumped about how a mortgage works (me included). ![]()
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