Blended rates and APRs are used on Mortgage Coach presentations to give the borrower an easier way to compare multi-lien scenarios. The calculation behind them is pretty straightforward and shows the weighted average interest rate (commonly called the blended rate) on two mortgages at differing interest rates: the average rate on these mortgages is 'weighted' by their respective loan amounts.
If I have a 1st mortgage of $100k at 5% and a 2nd mortgage at $40k for 6% and I want to find a blended rate, I would need to multiply each rate against its corresponding loan amount, then add them together and divide by the total balance to get my average rate. Here's how it looks written out:
[(100,000 x 5) + (40,000 x 6)] / 100,000 + 40,000
[500,000 + 240,000] / 140,000
[740,000 ] / 140,000 = 5.2857
This same blended calculation can be used to determine the blended APR as well. Just use the APR in place of the rate at each step.