# Is There a Blended Interest Rate?

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.

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