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Home Q & A Board Science-Related Homework Help Mathematics
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wilcoxj49 wilcoxj49
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6 months ago
A client has a first mortgage of $175,000 at 5.8% and a second mortgage of $25,000 at 6.7%. What is the weighted average rate of mortgage that the client pays?

▸ 5.9%

▸ 6.3%

▸ 6.5%

▸ 6%

▸ 6.2%
Textbook 
Business Mathematics in Canada

Business Mathematics in Canada


Edition: 11th
Authors:
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amieamie
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6 months ago
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5.9%


Excerpt
To calculate the weighted average rate of the mortgages, you need to consider both the first mortgage and the second mortgage based on their respective amounts.

Step 1: Calculate the interest paid on the first mortgage:

Interest on the first mortgage = Principal of the first mortgage * Interest rate of the first mortgage
Interest on the first mortgage = $175,000 * 5.8% = $10,150

Step 2: Calculate the interest paid on the second mortgage:

Interest on the second mortgage = Principal of the second mortgage * Interest rate of the second mortgage
Interest on the second mortgage = $25,000 * 6.7% = $1,675

Step 3: Calculate the total interest paid on both mortgages:

Total interest = Interest on the first mortgage + Interest on the second mortgage
Total interest = $10,150 + $1,675 = $11,825

Step 4: Calculate the weighted average rate:

Weighted Average Rate = Total Interest / Total Principal
Weighted Average Rate = $11,825 / ($175,000 + $25,000) = $11,825 / $200,000

Now, calculate the percentage:

Weighted Average Rate = ($11,825 / $200,000) * 100% = 5.9125%

Rounded to the nearest tenth, the weighted average rate of the mortgages that the client pays is approximately 5.9%. So, the correct answer is:

▸ 5.9%
This verified answer contains over 200 words.
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Anonymous
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4 months ago
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