Question

calculating the weighted average interest rate
weighted average spreadsheet setup
mondell reviews his financing options and decides to adjust the amounts
borrowed. he now takes $15,000 from the dealership at an interest rate of
4.5% and $10,000 from a personal line of credit at an interest rate of 5.5%.
mondell inputs his loan details into a spreadsheet to calculate the weighted
average interest rate.
if mendell entered the correct formula in cell d5 to calculate the weighted
average interest rate for his car loans, and the values in cells d4 and b4 are
$1,225 and $25,000 respectively, what would be the result displayed in cell
d5?

Explanation:

Step1: Calculate the weighted average interest rate formula

The formula for the weighted average interest rate \(r=\frac{\sum_{i = 1}^{n}A_{i}r_{i}}{\sum_{i=1}^{n}A_{i}}\), where \(A_{i}\) is the amount of each loan and \(r_{i}\) is the interest rate of each loan.

In the spreadsheet, the formula in cell \(D2\) is \(=B2*(C2 / 100)\) (for the dealership loan: \(A_1 = 15000\), \(r_1=4.5\%\)), so \(D2=15000\times\frac{4.5}{100}=675\).

The formula in cell \(D3\) is \(=B3*(C3 / 100)\) (for the personal loan: \(A_2 = 10000\), \(r_2 = 5.5\%\)), so \(D3=10000\times\frac{5.5}{100}=550\).

The total amount in cell \(B4\) is \(B4=SUM(B2:B3)=15000 + 10000=25000\).

The formula for the weighted - average interest rate (if we consider the general formula, and in the spreadsheet context, the value in \(D4\) is \(D4=D2 + D3=675+550 = 1225\))

The weighted - average interest rate \(r=\frac{D4}{B4}\times100\)

Step2: Substitute the values

Substitute \(D4 = 1225\) and \(B4=25000\) into the formula \(r=\frac{1225}{25000}\times100\)

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Answer:

\(4.9\%\)