Answer the following time value of money questions assuming the interest rate is 8 percent.

a. What is the present value of $1,000 to be received in four years?

b. What is the present value of $1,000 to be received in eight years? Why does the present value fall as the number of years increases?

c. What will be the value in seven years of $12,000 invested today?

d. How much would you pay for the right to receive $5,000 at the end of year 1, $4,000 at the end of year 2, and $8,000 at the end of year 5?

e. How long will it take for a $2,000 investment to double in value?

f. What will be the value in 20 years of $1,000 invested at the end of each, year for the next 20 years?