Puzzle #1 posed the question: given a $100,000 mortgage at 5% with monthly payments of $536.82 for 30 years, what is the average life of the principal payments? The puzzle was to be solved with just a few simple calculations.
The answer is:
(536.82 x 360 – 100,000) /(100,000 * .05) = 18.65 years.
The formula calculates total interest by subtracting the principal ($100,000) from the total payments ($536.82 x 360). The total interest is then divided by one year’s interest ($100,000 x 5%) to get the average amount of time that the principal is outstanding. This is the same as the average life of the principal payments. For a more complete discussion of Puzzle #1 and its implications, please see Puzzle #1: Epilogue.
Another example would be if the mortgage were 15 years, with a monthly payment of $790.79. Adapting the above formula, we get an average life of:
(790.79 x 180 – 100,000) /(100,000 * .05) = 8.47 years.
Now suppose the original mortgage (30 years, monthly payment of $536.82) pays on schedule for 15 years but then ends with a balloon payment. Can you figure out the principal average life, again with only a few basic calculations? Good luck!
Related Post: Puzzle #3: A Better Answer
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