Answer: The actual rate of the mortgage is 5.27%.
Since we're taking two mortgages for a total of $200,000 for 30 years, we can find the actual rate of the mortgage by finding the weighted average of the two rates. The weights in this case will be the proportion of loan taken at each rate
We have
Rates Weights Rates * Weights
4.15 0.80 [tex]4.15 * 0.80 = 3.32[/tex]
9.75 0.20 [tex]9.75 * 0.20 = 1.95[/tex]
Total 5.27%
