Monthly and Prepayment Formulas
Just as with ARMs:
Mortgages in which the interest rate can go up or down according to financial market conditions.
Example: A person who purchases a home with an ARM will have to pay more for the mortgage if interest rates go up., monthly and prepayment formulas come in handy with balloon mortgagesballoon mortgages:
A type of mortgage in which the final payment is considerably higher than preceding payments..
The monthly payment formula determines how much you’ll pay each month.
M=Pr(1+r)n/(1+r)n-1
The prepayment formula determines how much is left on the mortgage at the end of a set period of time.
A=P(1+r)h+M((1-(1+r)h)/r)
In each of these formulas, the variables are the same:
M = monthly payment
P = principal or amount of the loan
r = periodic interest rate
n = number of months in the loan period
h = number of payments already made
A = the unpaid balance after the hth payment
Note: Recall that you can also find the monthly payment by using a TVM Solver. The “bal(“ function on a typical calculator will tell you the amount left on a loan.
*THIS IS AN EXAMPLE TO HELP YOU
There are two parts to a balloon:
A type of mortgage in which the final payment is considerably higher than preceding payments.: the monthly payments over the life of the loan and the balloon payment itself. And the formulas used to find these payments should be very familiar to you. In fact, the calculation you just did was essentially finding the balloon payment.
The monthly payment formula calculates the monthly payments, and the prepayment formula calculates the balloon payment. Consider this example.
Sandra is considering a 7/23 balloon mortgage to purchase a house for $138,000. The interest rate is 4.5%. She needs to know what her monthly payments will be and the size of the balloon payment.
Finding the Balloon Payment
1. First, use the monthly payment formula to find the monthly payment to the nearest cent.
2. Her monthly payment is $699.23. What will her balloon payment be at the end of 7 years? Use the prepayment formula to find the amount to the nearest cent.
For Sandra’s 7/23 balloon mortgage situation, you saw that she will have the following payments:
• The monthly payment for the first 7 years is $699.23.
• The balloon payment is about $120,096.
3. What is her total payment over the life of the balloon mortgage?
When will her house be paid off?
All of this, of course, assumes that she can pay $120,096 after year 7. If she just had a typical 30-year mortgage fixed at the same interest rate, her payments would be $699.23 for 30 years rather than 7. In this case, her total cost for the house will be much higher: $251,722.80.
