August 19, 2002
"I am considering refinancing my 7.125% loan, which has a balance of
$375,000, into a $300,000 first mortgage at 6.5% and a $75,000 second
mortgage at 7.75%. My broker says that the blended rate of the two
mortgages is 6.75%, or well below 7.125%, so that this will save me
money. Is he right?"
Yes, although he hasn’t really given you a blended rate. His 6.75% is
the weighted average interest rate; the 6.5% rate is weighted by
300,000, and the 7.75% rate is weighted by 75,000. It is a decent
approximation.
The blended rate is the sum of all interest payments on the two
mortgages over a specified period, divided by the sum of all the
balances of the two mortgages over the same period. If the terms of the
two mortgages are the same, the blended rate will be the same as the
weighted average rate.
If the second mortgage carrying the higher rate has a shorter term,
however, which is common, the blended rate will be a little lower
because the higher rate loan is paid down faster. If your second
mortgage has a 15-year term, the blended rate over 15 years is 6.68%.
The conclusion (that the combination of two mortgages is the better
deal) remains intact.
The blended rate is an imperfect measure, however, because it does not
account for the time value of money. Interest paid in month one has the
same weight as interest paid in the last month. Furthermore, the blended
rate cannot take account of any difference in upfront costs between the
single mortgage and the two mortgages. A blended APR deals with both
problems.
The APR is a measure of interest cost over a specific period that allows
for the time value of money. Assuming no upfront costs in your case, the
blended APR is 6.70% over 15 years, which is very close to the blended
rate. But if there were differences in upfront costs, only the blended
APR would provide an accurate measure of cost.
If you can calculate a blended APR, therefore, there is no need to use a
weighted average rate or a blended rate. To get the spreadsheet that
calculates a blended APR, click on
Blended APR. You can
download this spreadsheet to your own computer.