1. Mortgages and Creating Amortization Tables
April 6th, 2011

2. When taking out a mortgage from the bank to purchase a house, you would first look into the amount of interest that would have to be paid back to the bank in addition to the principal amount borrowed.
An amortization schedule and table helps do just that. The table shows you how much your payment is, how much of that payment goes to interest, and how much of that payment is actually used to pay back the principal amount. 

3. Example:
Marshall and Vana buy a new house that costs $195,000. They have a down payment of $15,000 and apply for a mortgage for the remaining $180,000. The bank approves their mortgage and offers them a rate of 5.2%/a compounded monthly with required monthly payments of $1 300.

4. Payment # 1
When they make payment #1, one month’s interest is owed. To calculate the interest for one month, follow this formula:
, where

5. Therefore, the interest owed for month 1 is $780.
If they make a payment of $1 300 and $780 is interest, than they have only paid $520 off of the principal. ( = 520)
So if they are able to pay off $520 from their principal, they now owe $ ( = )  

6. Payment # 2
When they make payment #2, one month’s interest is owed. To calculate the interest for one month, follow this formula: Note: be sure you use your new principal calculated in the previous step. You do not want to be paying interest on $ when you no longer owe that much.

7. Therefore, the interest owed for month 1 is $777.75.
If they make a payment of $1300 and $ is interest, than they have only paid $ off of the principal.
( = )
So if they are able to pay off $ from their principal, they now owe $
( = ) 

8. All calculations for every month continue as shown in the handout.
Calculate the rows of the amortization table for rows 5 to 8.
How do the interest payments change with each additional payment (as you move down the table)?
How do the principal payments change with each additional payment?
How much interest did they pay in the first 5 months?
How much principal were they able to pay off in 5 months?

9. It often takes many years before a larger portion of your payment goes to paying off the principal rather than the interest?
As you can see a mortgage is very expensive - not only do you have to pay back the principal but you also have to pay back thousands of dollars in interest.  Now you will examine how much money (interest and principal) you have to pay when you take out a $ mortgage at 5.5%/a compounded semi-annually, amortized over 25 years.
Modified from

10. EX 2: Solve using the TVM Solver: Sarah and Fred just took out a $ mortgage at 5.5%/a compounded semi-annually and amortized over 25 years. What are Sarah and Fred’s monthly payments? Note for this problem pay close attention to the payments/year and compounding periods/year.