Question

linda plans to calculate the weighted average interest rate for the total mortgage by combining the interest rates of all three parts based on their proportions of the total mortgage amount. this will help her understand the overall cost of financing her home purchase.
portion a:
amount: $100,000
interest rate: 3.0% per annum
portion b:
amount: $150,000
interest rate: 3.5% per annum
portion c:
amount: $50,000
interest rate: 4.0% per annum
mortgage total: $300,000
portions and interest rates:
is the formula in cell c6 = d5 * 100 that calculates the overall weighted average interest rate, correct?

Explanation:

Step1: Calculate the weight of each portion

The total mortgage amount \(D5 = 100000 + 150000+50000=\$300000\)
For Portion A: \(weight_A=\frac{100000}{300000}=\frac{1}{3}\)
For Portion B: \(weight_B=\frac{150000}{300000}=\frac{1}{2}\)
For Portion C: \(weight_C=\frac{50000}{300000}=\frac{1}{6}\)

Step2: Calculate the weighted - average interest rate

The formula for the weighted - average interest rate \(r\) is \(r = weight_A\times r_A+weight_B\times r_B + weight_C\times r_C\)
where \(r_A = 3.0\%\), \(r_B=3.5\%\), \(r_C = 4.0\%\)
\(r=\frac{1}{3}\times3.0\%+\frac{1}{2}\times3.5\%+\frac{1}{6}\times4.0\%\)
\(r = 1.0\%+1.75\%+\frac{4.0\%}{6}\)
\(r=1.0\% + 1.75\%+0.67\%\)
\(r = 3.42\%\)

The formula \(C6 = D5*100\) is incorrect. The formula should be based on the weighted - sum of \((\text{amount}_i\times\text{interest rate}_i)/\text{total amount}\)

Answer:

No, the correct formula should be based on the weighted - average of the interest rates considering the proportion of each loan amount. The formula \(C6 = D5*100\) is wrong.