# Advanced NPV Problems

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Advanced Time Value of Money Problems
Professor A. Spieler

Question 1 (mortgage problem)
(Try to work this question WITHOUT using Excel)

You purchase a house that costs \$625,000 with an 8%, 30-year mortgage. You make a 20% down payment to avoid PMI insurance.

1. What is your monthly payment?

2. Amortize the first and second payments.

3. What is the mortgage balance after 5 years?

4. What percentage of the principal is paid off after 5 years?

5. Suppose after 5 years you refinance at 6% the remaining balance at a cost of \$10,000, for 30 years. What is your new monthly payment?

6. Further, suppose you maintain the same payments as in (1), i.e. pre-pay on the principal, how many YEARS until you payoff the mortgage?

Question 2 (2nd mortgage problem)
You are considering the purchase of a \$500,000 home. You plan to take a 30-year fixed mortgage after making a 20% downpayment to avoid PMI. Payments are to be made monthly (at the end of the month) and the APR is 8%.

1. What is the monthly payment?

2. During what month does the principal portion first exceed the interest portion? Are you surprised by your answer?

3. How long does it take to pay off your mortgage if you pay an additional \$300 towards principal each payment?

4. How long does it take to pay off your mortgage if you pay an additional amount each month equal to the current month’s principal?

Question 3 (College planning)
Your child was just born and you are planning for his/her college education. Based on your wonderful experience in Financial Economics you decide to send your child to Hofstra University as well. You anticipate the annual tuition to be \$60,000 per year for the four years of college. You plan on making equal deposits on your child’s birthday every year starting today, the day of your child’s birth. No deposits will be made after starting college. The first tuition payment is due in exactly 18 years from today (the day your child turns 18 – no deposit required, i.e. last

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