Consider your parent's home mortgage: 10 years ago your parents purchased a $240,000 home. At the time they paid 10% as a down payment, and borrowed the remaining 90% via a 30 year mortgage with a fixed interest rate of 6% APR. Payments were made monthly and are of a constant size each month. The first payment was paid one month after the purchase. Note: In many countries (for example, in the U.S.) on your personal taxes, you can often deduct interest paid on a home-which effectively lowers the amount you have to pay in taxes. Therefore, understanding how to compute interest paid month by month (and adding up the 12 months that comprised the tax year) is useful when it comes time to pay your taxes.

Note (Cont.): keep precision high, using 6 significant digits.

A) How long does it take to pay off just over half of the mortgage? That is, how many monthly payments must be made (in total) to pay off just over half of the initial amount borrowed?

Hint: You know how much you owe (approximately half of the initial principal) and you're trying to determine how many payments have been made to get there. In this problem, you'll be solving for "n" as an exponent (using logs). The value you get for "n" will not be a whole number, but will need to make it into a whole number (ex: might get 132.543, need to determine if the value is n=132 or n=133. You can check which value is correct by computing the present value using each value of n, and then selecting the value of n that results in a present value just below half of the initial principal (if you are paying off just over half, then just under half will remain).

B) Context: Now that ten years have gone by (since home purchase), your parents have just paid their 120th monthly payment (paid today). After this payment, they owe $180,761.00 on the mortgage as of now. For the 121st payment (due in one month), what proportion of the payment will be associated with interest paid? (Express the answer as a decimal, not as a percent).

C) Between the 250th and 251st payments, how much principal is still outstanding? (answer in dollars and cents)