My Math Forum Average Weighted Interest Rate

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 July 25th, 2018, 12:20 AM #1 Newbie   Joined: Jul 2018 From: Belgium Posts: 1 Thanks: 0 Average Weighted Interest Rate Dear, I've got a problem which I am unfortunately unable to solve. How can I compare the 3 loans below, to get an Average Weighted interest rate? Loan 1 Loan: 100.000 Residual Value: 0 Period: 60 months Nominal Interest Rate : 2% Loan 2 Loan: 50.000 Residual Value: 10.000 Period: 72 months Nominal Interest Rate : 3% Loan 3 Loan: 80.000 Residual Value: 20.000 Period: 84 months Nominal Interest Rate : 4% Thanks in advance Rikik Last edited by skipjack; July 25th, 2018 at 12:55 AM.
 July 25th, 2018, 04:23 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 The standard definition of a weighted mean is: The sum of the products of the "weights" and "data" divided by the sum of the "weights." In this case, the data are the interest rates on each loan, and the weights are the amounts of each loan. If we ask how much interest are you paying overall, we calculate: $(100000 \times 0.02) + (50000 \times 0.03) + (80000 \times 0.04) = \\ 2000 + 1500 + 3200 = 6700.$ That is a sum of products, with the "data" being the rates and the "weights" being the balance due. If we ask how much is your indebtedness, we calculate: $100000 + 50000 + 80000 = 230000.$ That is the sum of the weights $6700 \div 230000 \approx 2.9\%.$ So the weighted average tells us what the interest rate would need to be on a loan equal in amount to the total of three actual loans with a single interest payment equal to the total of the three actual payments due.
 July 25th, 2018, 04:36 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,337 Thanks: 1024 (100*2 + 50*3 + 80*4) / (100 + 50 + 80) = ~2.913% That's all that can be calculated. If you're looking for something else, then explain stuff like "residual value" (sounds like depreciation!) and "nominal rate" (simple interest?).
July 25th, 2018, 05:28 AM   #4
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 Originally Posted by Denis (100*2 + 50*3 + 80*4) / (100 + 50 + 80) = ~2.913% That's all that can be calculated. If you're looking for something else, then explain stuff like "residual value" (sounds like depreciation!) and "nominal rate" (simple interest?).
I suspect that this is background for a multi-question problem that goes on to ask for things like weighted average maturity.

One does wonder why no explanation on how to make such calculations was provided before posing the question.

 July 25th, 2018, 08:19 AM #5 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,337 Thanks: 1024 Jeff ya bad boy...ya sneaked in ahead of me aNUTter way: Average annual balances over the 7 years: 100*5 / 7 = 71.4 (50*6 - 10 - 10) / 7 = 40.0 (80*7 - 20) / 7 = 77.2 Average rate: (71.4*.02 + 40*.03 + 77.2*.04) / (71.4 + 40 + 77.2) = .0303.... or ~3% Reeeely my dear, who gives a damn

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