# Work shown

1. You have just received a windfall from an investment you made in a friend’s business. She will be paying you \$35,743 at the end of this year, \$71,486 at the end of the following year, and \$107,229 at the end of the year after that (three years from today). The interest rate is 13.3% per year.
a. What is the present value of your windfall?
b. What is the future value of your windfall in three years (on the date of the last payment)?

2. Your grandfather has been putting \$4000 into savings account on every birthday since your first (that is when you turned 1). The account pays an interest rate of 3%. How much money will be in the account immediately after your grandmother makes the deposit on your 18th birthday?

3. You want to endow a scholarship that will pay \$12,000 per year forever, starting one year from now. If the school’s endowment discount rate is 5%, what amount must donate to endow the scholarship?

4. Assume that Social Security promises you \$31,000 per year starting when you retire 45 years from today (the first \$31,000 will come 45 years from now). If your discount rate is 10%, compounded annually, and you plan to live for 12
years after retiring (so that you will get a total of 13 payments including the first one), what is the value today of Social Security’s promise?

5. In 1975 interest rates were 7.85% and the rate of inflation was 12.3% in the US. (Note:Be careful not to round any intermediate steps less than six decimal places.)
a. What was the real interest rate in 1975?

6. Suppose Oppenheimer Bank is offering a 30- year mortgage with an EAR of 6.625%. If you plan to borrow \$275,000, what will your monthly payment be? (Note: Be careful not to round any intermediate steps less than six decimal places.)

7. If the rate of inflation is 4.7%, what nominal interest rate is necessary for you to earn a 2.3% real interest rate on your investment? (Note: Be careful not to round any intermediate steps less than six decimal places.)