MORTGAGE CALCULATORS(More Info)
A STEP BY STEP APPROACH © 2005 - 2007

Step 3: The Next Level
Compare Two Mortgages (Type 2)

Let us now compare two amortizing loans with all the same terms except the interest rate and also let us anticipate that we will sell the property in 8 years and pay off the loan early. Now click here for COMPARE TWO MORTGAGES (Type 2). The default "Mortgage Terms" for both loans is 30 years. The default rate for the new loan is 4.125% and the default rate for the old is 5.125%. The default value for "How Long Do You Expect To Live In The Home?" is 30, however change this to 8. Generating the results will then show 1) a difference in the rates of 1.00%, 2) a difference in the monthly payment of $59.84, 3) a difference in total interest payments over the life of the two loans of $7,841, and 4) a difference in total payments (principal & interest) over the life of the two loans of $7,841. The schedule at the bottom will display the details relating to the differences in the annual payments. You will see that at the end of the 8th year both loans will stop and the difference in the payments for the 8th year will be $2,815.

This is a great little analysis. The difference between the results in Step 2 and in Step 3 ($21,541 - $7,841) or $13,700 represents the lost opportunity benefit for closing out the loan early in the 8th year rather then holding the loan until maturity. This analysis is relatively 1) clean and 2) straight forward, but 3) NOT so easy to interpret.

It is not so easy to interpret because many people get somewhat confused by the difference in the payments in the 8th year (the year the payoff of the loan occurs) or $2,815. They expect the difference to be the same in the 8th year as in all of the prior years, i.e. the difference in the monthly payment multiplied by 12 months or ($59.84 x 12) or $718. The reason for this additional difference ($2,815 - $718) or $2,097 is the result of less principal balance being owed on the new mortgage versus the principal balance being owed on the old mortgage in the 8th year.

Why does this occur? This has to do with the rate at which the principal balance declines in the two amortizing loans. If we compare the two loans, the lower interest rate loan's principal balance will decline more rapidly in the earlier years than the higher interest rate loan, and the higher interest rate loan's principal balance will decline more rapidly in the later years than the lower interest rate loan.

However there are some limitations to this type of simple mortgage calculator; i.e. 1) no ability to adjust for a loan which may have already begun amortizing, and 2) no ability to adjust for the effects of present value and the time value of money.

Step 4: Intermediate
Compare Two Mortgages (Type 3)

Let us now compare two 30 year amortizing fixed rate loans, an old loan and a new loan. The new loan will have a principal balance of $100,000 and we will assume the old loan (the current existing loan on the property) was originally $105,000, has been amortizing for 3 years and has a remaining principal balance of $100,214. Now click here for COMPARE TWO MORTGAGES (Type 3). The default "Mortgage Terms" for both loans is 30 years. The default rate for the new loan is 4.125% and the default rate for the old is 5.125%. The default balance for the new loan is $100,000 and for the default balance for the original old loan is $105,000. The default remaining principal balance on the old loan is $100,214. The default value for "How Long Do You Expect To Live In The Home?" is 30. Leave this at 30 for now.

Now generating the results will show 1) a difference in the rates of 1.00%, 2) a difference in the monthly payment of $87.06, 3) a difference in total interest payments over the life of the two loans of $10,547, 4) a difference in total payments (principal & interest) over the life of the two loans of $10,761, and 5) a difference in the term of the loans of 3.0 years or (30.0 - 27.0). The schedule at the bottom will display the details relating to the differences in the annual payments. You will see that at the end of the 27th year the original loan will stop because it has fully amortized and the difference in the payments in years 28, 29, and 30 will be $5,816.

This is a great little analysis. This analysis is relatively 1) clean, but 2) NOT so straight forward, and 3) NOT so easy to interpret.

However there are some limitations to this type of simple mortgage calculator; i.e. 1 ) no ability to adjust for the effects of present value and the time value of money.

Step 5: Considering Present Value
Compare Two Mortgages Using PV (Type 1)

Let us now consider present value or the time value of money. We are going to apply present value to the results generated in Step 2. Again, compare two amortizing loans with all the same terms except the interest rate. So click here for COMPARE TWO MORTGAGES USING PV (Type 1). The default balances for the both the new loan and old loan are $100,000. The default "Mortgage Terms" for both loans is 30 years. The default rate for the new loan is 4.125% and the default rate for the old is 5.125%.

However there are two additional input fields; 1) an input field for a discount rate, and 2) an input field for the costs to close the loan. The discount rate field has a default value of 5.125% and the "costs to close the loan" field has a default value of $2,500. For now just leave these set to their default values.

Generating the results will show 1) a difference in the rates of 1.00%, 2) a difference in the monthly payment of $59.84, 3) a difference in total interest payments over the life of the two loans of $21,541, 4) a difference in total payments (principal & interest) over the life of the two loans of $21,541, 5) a present value of $11,136, 6) a cost to refinance of $2,500, and 7) a net of $8,636. The schedule at the bottom will display the details relating to the differences in the annual payments and the present value of each of those differences.

Please note the following important assumptions:

1) Closing costs of the loan, which would include lawyer's fees, title insurance, loan application fees, appraisal fees and any other fees associated with closing and processing the loan.

2) In determining a discount rate we assume a flat yield curve. It would be much too complex to construct a yield curve using current treasury prices by applying a process referred to as cubic splining and then subsequently discounting the difference in the cash flows between the two mortgages using the various rates along the curve that coincide with the various cash flows. It is deemed sufficient for consumer purposes to assume a flat yield curve. If you are the average consumer and you read the above paragraph then your head is probably spinning, but if you are a professional trader of bonds then you have probably interpreted what I wrote.

This is a great little analysis. It is 1) clean, 2) straight forward, and 3) relatively easy to interpret.

However there are some limitations to this type of mortgage calculator; i.e. 1) no ability to adjust for an early pay off of the loan, and 2) no ability to adjust for a loan which may have already begun amortizing.

In comparing the result from Step 2 to the results here in Step 5, it becomes apparent that the time value of money can have a significant effect on the results. The difference in the cash flows between the two mortgages is $21,541, but the present value of the differences in cash flows is $11,136. Subtract the cost to refinance of $2,500 and we are left with $8,636. This further assumes that we will hold the property and the loan until maturity.

If you are interested in applying an adjustment for terminating the loan before maturity then try these two calculators, COMPARE TWO MORTGAGES USING PV (Type 2) and COMPARE TWO MORTGAGES USING PV (Type 3).

Click here to continue reading on the next page.


By Using This Website You Agree That You Have Read and Understand Our Disclaimer!
Analytical Finances, Inc. Contents © 2005 - 2007
Mortgage Models / Mortgage Calculators / Mortgage Information / Mortgage Amortization / Mortgage Interest Rates / Contact Us