Here is the first in a series of puzzles that might have something to do with finance or math. The first to respond with a correct answer will be recognized in The Well-Tempered Spreadsheet Hall of Really Smart People.
First, let’s be clear about the concept of average life of a cash flow. The average life is the average amount of time from a starting date to future cash flows, as weighted by those cash flows. For example, if there is a $100 cash flow in 1 year and a $300 cash flow in 2 years, the average life is (1 year x $100 + 2 years x $300)/$400 = 1.75 years.
Suppose there is a $100,000 mortgage at 5% with monthly payments of $536.82 for 30 years. Each monthly payment breaks down differently into a principal payment and an interest payment.
Here’s the question:
What is the average life (in years) of the principal payments?
Not hard, just a pain to set up a 360 row mortgage schedule and multiply the principal payments by the month numbers, etc.
But here’s the catch: You can’t use a spreadsheet! This is an unspreadsheet problem, as the Mad Hatter might say.
You must find the answer with no more than five calculations on a basic calculator.
Please show your work. Good luck!
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