How much would you have to invest today to receive the following? Use Appendix B or Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods.

a. $15,500 in 12 years at 11 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

b. $20,000 in 19 years at 7 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

c. $8,100 each year for 18 years at 15 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

d. $56,000 each year for 25 years at 8 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)