Problem 9-11 Future value [LO2] If you invest $8,500 per period for the followin
ID: 1172018 • Letter: P
Question
Problem 9-11 Future value [LO2] If you invest $8,500 per period for the following number of periods, how much would you have: Use Appendix Cas an approximate answer, but calculate your final answer using the formula and financial calculator methods. a. In 12 years at 10 percent? (Do not round intermediate calculations. Round your final answer to 2 decimal places.) b. In 50 years at 9 percent? (Do not round intermediatecalculations. Round your final answer to 2 decimal places.) Input variables: Annuity payment a. Number of years a. Interest rate b. Number of years b. Interest rate a. Appendix value b. Appendix value $8,500 12 years 0.10 50 years 0.09 21.384 815.08 Solution and Explanation: Future value b. Future value Appendix values: b.Explanation / Answer
(a)
Annuity amount = $ 8,500
Time period = 12 years
Interest rate = 10%
Future value of annuity = Annuity amount [{ ( 1 + r )n - 1 } / r]
= 8,500 [ { (1 + 0.10 ) 12 - 1 } / 0.10 ]
= 8,500 [ {( 1.10 ) 12 - 1 } / 0.10 ]
= 8,500 [ { 3.1384 - 1 } / 0.10 ]
= 8,500 x 21.3843
= $181,766.55
Appendix value = Annuity amount x CVAF (10%, 12 )
= 8,500 x 21.384
= $ 181,764
(b)
Annuity amount = $ 8,500
Time period = 50 years
Interest rate = 9%
Future value of annuity = Annuity amount [{ ( 1 + r )n - 1 } / r]
= 8,500 [ { (1 + 0.09 ) 50 - 1 } / 0.09 ]
= 8,500 [ {( 1.09 ) 50 - 1 } / 0.09 ]
= 8,500 [ { 74.3575 - 1 } / 0.09 ]
= 8,500 x 815.0835
= $6,928,210.23
Appendix value = Annuity amount x CVAF (9%, 50 )
= 8,500 x 815.08
= $ 6,928,180