New Loans

Example 1 - Borrow $48,000 for 15 years at a 9.5% annual interest rate

Figure 1 shows where to type the numbers for a $48,000 mortgage for 15 years at an annual interest rate of 9.5%. The only Find button enabled is beside Monthly Payment. If you were to click it you'd see what your monthly payment would be (excluding insurance and tax escrow). See Figure 3 for the resulting monthly payment: $501.23. The total interest, $42,221.00, and the total paid, $90,221.00, are also shown. Clicking the Show Report button would show a repayment schedule.

Example 2 - How much can I borrow if I can afford $800 monthly payments?

You can determine how much principal you can borrow for a given interest rate, duration and monthly payment. Suppose you can afford an $800 per month payment (excluding insurance and tax escrow) and the current interest rate is 5.125% for a 30 year loan. Enter the three known numbers, 800, 5.125 and 30 in the appropriate places and click the principal Find button. You will see $146,927.30 for the principal. The total interest paid is $141,072.70 and the total paid is $288,000.00.

If you then want to know how much you can borrow if a 25 year loan has a 5.000% interest rate: Enter 25 for the duration, 5 for the annual interest rate (there is no need to retype the monthly payment) and click the principal Find button to see $136,848.04 for the new principal, $103,151.96 for the total interest and $240,000.00 for the total paid. By taking a 25 year loan you would reduce the principal you can borrow by about $10,000 but you would save about $28,000 in total interest paid in this example.

Existing Loans

Example 3 -  Principal prepayment

Mortgage can find a new duration for your loan if you prepay principal on it. If you add, say $100, to your monthly payment, the lender will use it to pay down the remaining principal. The lender changes the duration of the loan, though in a subtle way,* so you can click the duration Find button to find how soon you will pay the loan off. It is accurate if you pay the extra amount throughout the entire (shortened) duration of the loan.

If you want to add an additional amount to the principal potion of each months payment, increase the monthly payment by that amount and click the duration Find button. The increase will be applied to the each months principal portion of the payment. The Report will reflect the change. If you have a 30 year, $100,000 loan at 5% interest, your monthly payment is normally $536.83. Use Mortgage to verify this amount. Then to see the effect of prepaying $100 per month, first add $100 to $536.83, yielding $636.83. Type $636.83 in for the monthly payment amount and click the duration Find button. Mortgage shows the loan would be paid off in 21.287 years, or about 21 years and three months. The total paid with $100 prepayment per month is  $30,582.25 less than without prepayment.

The upshot: You can change only the monthly payment on an existing loan, by paying more each month, so don't change the principal or interest rate in Mortgage when working with an existing loan. Increasing your monthly payment will shorten the duration of the loan, so clicking the duration Find button is okay.

Of course clicking any Find button is valid when you are considering a new loan or refinancing an existing loan.  It should be obvious that clicking the interest Find button does not change the interest rate lenders are currently charging on new loans; it tells you the interest rate required for the other numbers to be a valid combination.

Example 4 - Refinance an existing loan

To evaluate refinancing an existing loan, take the remaining principal from the existing loan and enter it in Mortgage as Principal. Enter the new annual interest rate and duration advertised by a lender. Click the monthly payment Find button to see the new monthly payment, total interest and total paid.

*This is the subtle cause of duration change: When you make normal monthly payments, the lender charges you each month for that month's interest on the entire remaining principal. The lender arranges the monthly payment amount ahead of time so it covers all the interest on the principal for first month plus a small amount on the principal. The next month the principal is a little smaller due to the first month's principal paid, so the interest paid for that month is a little smaller, and the principal paid is a little larger. This continues throughout the life of the loan. Because the remaining principal gets smaller each month, the interest on it gets smaller and thus the principal paid each month gets larger.

But if you prepay an additional amount – say $100 – on the principal each month, the amount of the principal for succeeding months will be smaller than the lender planned, so the interest paid for each succeeding month is less, the principal paid is more, and the loan is paid off faster. That doesn't change the interest rate the lender is charging, or the initial principal, though.

The lender does not change your interest rate because you prepay on your principal on an existing loan.  So clicking the interest rate Find button is not valid then. Likewise, clicking the principal Find button obviously does not change the amount of money you borrowed initially on an existing loan. It tells you how much you could borrow on a new loan for the given duration, interest rate and monthly payment.

Copyright 2008-2010 by Ron Charlton