Question

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

  
a. $12,500 in 7 years at 11 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

b. $16,100 in 15 years at 10 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

c. $6,250 each year for 14 years at 8 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

d. $43,000 each year for 30 years at 6 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

Answer 1

Question a:

FV = Amount to receive = $12,500

n = 7 years

r = interest rate = 11%

Amount to be invested today = FV / (1+r)^n

= $12,500 / (1+11%)^7

= $12,500 / 2.07616015

= $6,020.73015

Therefore, amount to be invested today is $6,020.73

Question b:

FV = Amount to receive = $16,100

n = 15 years

r = interest rate = 10%

Amount to be invested today = FV / (1+r)^n

= $16,100 / (1+10%)^15

= $16,100 / 4.17724817

= $3,854.21199

Therefore, amount to be invested today is $3,854.21

Question c:

P = Annual payment = $6,250

n = 14 years

r = interest rate = 8%

Amount to be invested today = P * [1 - (1+r)^-n] / r

= $6,250 * [1 - (1+8%)^-14] / 8%

= $6,250 * 0.659538959 / 0.08

= $51,526.4811

Therefore, amount to be invested today is $51,526.48

Question d:

P = Annual payment = $43,000

n = 30 years

r = interest rate = 6%

Amount to be invested today = P * [1 - (1+r)^-n] / r

= $43,000 * [1 - (1+6%)^-30] / 6%

= $43,000 * 0.825889869 / 0.06

= $591,887.74

Therefore, amount to be invested today is $591,887.74