Question

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. $13,500 in 10 years at 11 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

b. $17,250 in 16 years at 14 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

c. $6,900 each year for 19 years at 9 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

d. $46,000 each year for 25 years at 13 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

Answer 1

(a)-Present Value of $13,500 in 10 years at 11 percent.

Present Value = Future Value / (1 + r)ⁿ

= $13,500 / (1 + 0.11)¹⁰

= $13,500 / 2.839420

= $4754.49

(b)- Present Value of $17,250 in 16 years at 14 percent.

Present Value = Future Value / (1 + r)ⁿ

= $17,250 / (1 + 0.14)¹⁶

= $17,250 / 8.137249

= $2,119.88

(c)- Present Value of $6,900 each year for 19 years at 9 percent.

Present Value of Ordinary Annuity = P x [{1 - (1 / (1 + r) ⁿ} / r]

= $6,900 x [{1 - (1 / (1 + 0.09)¹⁹} / 0.09]

= $6,900 x [{1 - (1 / 5.141661)} / 0.09]

= $6,900 x [(1 - 0.194490) / 0.09]

= $6,900 x [0.805510 / 0.09]

= $6,900 x 8.950115

= $61,755.79

(d)- Present Value of $46,000 each year for 25 years at 13 percent.

Present Value of Ordinary Annuity = P x [{1 - (1 / (1 + r) ⁿ} / r]

= $46,000 x [{1 - (1 / (1 + 0.13)²⁵} / 0.13]

= $46,000 x [{1 - (1 / 21.23054)} / 0.13]

= $46,000 x [(1 - 0.047102) / 0.13]

= $46,000 x [0.952898 / 0.13]

= $46,000 x 7.329985

= $337,179.31