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Question: Your friend tells you he has a very simple trick for taking one-third off the time it takes to repay your mortgage: Use your Christmas bonus to make an extra payment on January 1 of each year (that is, pay your monthly payment due on that day twice). If you take out your mortgage on July 1, so your first monthly payment is due August 1, and you make an extra payment every January 1, how long will it take to pay off the mortgage? Assume that the mortgage has an original term of 30 years and an APR of 12%. (Hint: The original balance does not matter in this problem, so you can pick any number you want. In this case we will use $100,000 as the principal balance.) Note: Be careful not to round any intermediate steps less than six decimal places.

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