Explanation:
First, calculate the interest paid on each mortgage:
For the first mortgage of $175,000 at 5.8%:
Interest = Principal x Rate
Interest = $175,000 x 0.058 = $10,150
For the second mortgage of $25,000 at 6.7%:
Interest = Principal x Rate
Interest = $25,000 x 0.067 = $1,675
Now, calculate the total interest paid on both mortgages:
Total Interest = Interest on First Mortgage + Interest on Second Mortgage
Total Interest = $10,150 + $1,675 = $11,825
Next, calculate the total principal amount of both mortgages:
Total Principal = Principal of First Mortgage + Principal of Second Mortgage
Total Principal = $175,000 + $25,000 = $200,000
Now, calculate the average rate using the formula:
Average Rate = Total Interest / Total Principal
Average Rate = $11,825 / $200,000 ≈ 0.059125 or 5.9125%
So, the average rate of the mortgages that the client pays is approximately 5.9125%.