Each of the problems below provides practice with present value calculations.

a. At an annual interest rate of 3.5 percent, what is the present value of a single payment of $1000 to be received one year from now?

b. At an annual interest rate of 3.5 percent, what is the present value of a single payment of $1000 to be received three years from now?

c. At an annual interest rate of 3.5 percent, what is the present value of a stream of payments of $1000, each to be received at the end of one year, two years, and three years?

d. What is the present value of a lottery prize that pays you $1 million today plus $1 million one year from now plus $1 million two years from now?

e. How much would you need to deposit today in a bank account paying 4 percent interest if you want to withdraw $5000 one year from now?

f. If your friend offers to loan you $12 000 today to buy a used car, and wants you to repay him $13 500 in two years, should you accept this offer? The market interest rate on a loan from the bank is 4 percent.