Assignment:
Problem 1
Samantha opened a savings account this morning and made one deposit. At a 4% annual interest (EAR), her account balance will be $5,600 in exactly 5 years. Assume that she will not make any withdrawals or deposits, and ignore service charges and taxes. Please answer "True" or "False" to the following statements and briefly explain why.
a. Samantha deposited less than $5,600 this morning.
b. The present value of Samantha account is $5,600.
c. Samantha will earn an equal amount of interest every year for the next five years.
d. Samantha's account balance will be about $5,177.5 after two years.
Problem 2
Today is Jan 1, 2019. You are scheduled to receive annual payments of $6,000 for each of the next 6 years. The effective annual discount rate is 12 percent; all cash flows will be made at the end of each year, starting on Dec 31, 2019.
i. What is the present value of these cash flows?
ii. What is the PV of the cash flows if you are to receive these payments at the beginning of each year rather than at the end of each year
Problem 3
Go to www.zillow.com and find any property listing in the US. Find the listing price and estimated monthly mortgage payment provided by the website (Zillow assumes a 20% down payment and a 30-year fixed loan). Use the information to complete the following table, and then answer the questions below.
Property Listing Price:
Loan Amount (after 20% down payment):
Interest Rate (APR, monthly compounded):
Monthly Mortgage Payment:
a. What is the EAR corresponding to the APR? What is the effective monthly rate? Which rate should you use to calculate the monthly mortgage payment?
b. Please use your financial calculator to verify the monthly mortgage payment (assuming a 30-year fixed loan and 20% down payment). How much more does a homebuyer have to pay if the APR was up by 1%?
c. Other than the mortgage payments, can you think of other expenses or payments related to buying a property? What do you think is the minimum income for a home-buyer to safely afford this property? Please briefly explain your answer; for simplicity, you can ignore income taxes.
Problem 4
Joey receives two job offers: Job A has a starting annual salary of $80,000 and an expected annual salary growth of 7%. Job B has a starting annual salary of $100,000 and an expected salary growth of 5%. Joey is 30 years old and plans to retire when he turns 65. Ignore bonuses, pensions, other compensations and taxes; all cash flows will be made at the end of each year. Joey discounts future cash flows at an effective annual rate of 10%.
a. Which offer has a greater present value?
b. If Joey plans to retire when he turns 55 years old, which offer has a greater present value?
c. If we consider income taxes, could your answers to (a) and (b) be different? Why?
Note: qualitative analysis without numbers would suffice for (c).
Problem 5
Gloria wants to buy a helicopter drone as a birthday gift for her son. The marked price is $600, but if she makes a full payment today she can get an 8% discount off the marked price. Alternatively, the store offers a 12-month "interest-free" financing option: Gloria can pay $50 right now, and make eleven monthly payments of $50 (at the end of the future 11 months). What is the implied EAR of the financing option?