Your friend tells you he has a very simple trick for taking one-third of the time it takes to repay your mortgage: Use your holiday bonus to make an extra payment on January 1 of each year (that is, pay your monthly payment due on that day twice). Assume that the mortgage has an original balance of

$100,000,

has an original term of

30

years, and has an APR of

12.0%.

a. If you take out your mortgage on January 1 (so that your first payment is due on February 1), and you make your first extra payment at the end of the first year, in what year will you finish repaying your mortgage?

b. If you take out your mortgage on July 1 (so that the first payment is on August 1), and you make the extra payment each January, in how many months will you pay off your mortgage?

c. How will the amount of time it takes to pay off the loan given this strategy vary with the interest rate on the loan?

Note:

Make sure to round all intermediate calculations to at least 6 decimal places.