Question

Gail wants to buy a property with a first mortgage of $395,000 at 7.25% compounded semi-annually not in advance, and a second mortgage of $200,000 at 3.95% interest compounded semi-annually, not in advance. What is the average mortgage rate for the two mortgages (rounded to one decimal place)?

a) 5.9%
b) 6.1%
c) 6.3%

Answer 1

The average mortgage rate for the two mortgages is calculated using the weighted average formula and results in 6.1% when rounded to one decimal place.

Step-by-step explanation:

To calculate the average mortgage rate for the two mortgages held by Gail, we need to use the weighted average formula, taking into account the different mortgage amounts and their respective interest rates. The first mortgage has an amount of $395,000 with an interest rate of 7.25%, and the second mortgage has an amount of $200,000 with an interest rate of 3.95%. Thus, we can calculate the weighted average interest rate as follows:
(First mortgage interest rate × First mortgage amount + Second mortgage interest rate × Second mortgage amount) / (First mortgage amount + Second mortgage amount).
Substitute the given values to get: (7.25% × $395,000 + 3.95% × $200,000) / ($395,000 + $200,000).
Let's perform the calculation:
(0.0725 × $395,000 + 0.0395 × $200,000) / $595,000 = ($28662.5 + $7900) / $595,000 = $36,562.5 / $595,000 = 0.06145.
So, the average mortgage rate when rounded to one decimal place is 6.1% (b).