Suppose the Hempstead Savings Bank is offering 6% on all deposits and your initial deposit is $10,000.
(i) What is the balance in your savings account after 1 year?
(ii) What is the balance in your savings account after 5 years
(iii) How much interest has accumulated after 10 years?
(iv) How much do you have in your savings account after 6 months?
Suppose the Uniondale Savings Bank is offering 5% on all deposits and your initial deposit is $10,000.
(i) What is your balance after 5 years? You MUST use the Financial Tables to calculate your answers.
(ii) What is your balance after 8 years? You MUST use the Financial Tables to calculate your answers.
(iii) What is your balance after 5 years if the bank only offers simple interest?
Suppose you are expected to receive $10,000 in exactly 10 years. Find the present value under the following conditions. Assume the APR = 12%
(i) Annual compounding
(ii) Semi-annual compounding
(iii) Monthly compounding
You just graduated Hofstra University. Instead of saving for your retirement, you decide to purchase a new sports car for $40,000. Assume your first payment is one month from now and the loan is for 5 years.
(i) If the APR is 2.9%, what are your monthly payments? What is the EAR? (ii) If the APR is 9.9%, what are your monthly payments? What is the EAR?
Suppose the Bloomington Savings Bank is offering 6% on all savings deposits. Your initial deposit is $10,000.
(i) What is your balance after one year assuming annual compounding?
(ii) What is your balance after one year assuming semi-annual compounding?
(iii) What is your balance after one year assuming monthly compounding?
(iv) What is your balance after one year assuming daily compounding?
TIME VALUE OF MONEY ADVANCED PROBLEMS
Question 1 (mortgage problem)(Try to work this question WITHOUT using Excel)
You purchase a house that costs $625,000 with a 8%, 30-year mortgage. In order to avoid PMI insurance, you decide to follow a conforming mortgage by making a down payment of 20%.
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 pay off 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 deposit is on 17th birthday). Assume the annual expected return on your investments is 10% over this period.
1. Calculate the annual deposit. FV (deposits) = PV (tuition payments)
2. Calculate the amount needed if only equal annual deposits are made on birthday’s 5-10 inclusive.
FV (deposits) = PV (tuition payments as lump sum)
3. Calculate the amount needed if two equal annual deposits are made on birthday’s 5 and 13.
4. Answer part (i), now assume tuition rises 10% per year.
5. Answer part (i) assuming first deposit will be made on your child’s 1st birthday. All other information is the same. What is the annual tuition payment? How does it compare to part (i)? Is your answer surprising?
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