You wish to retire in 12 years, at which time you want to have accumulated enoug
ID: 2714824 • Letter: Y
Question
You wish to retire in 12 years, at which time you want to have accumulated enough money to receive an annual annuity of $27,000 for 17 years after retirement. During the period before retirement you can earn 8 percent annually, while after retirement you can earn 10 percent on your money.
What annual contributions to the retirement fund will allow you to receive the $27,000 annuity? Use Appendix C and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
What annual contributions to the retirement fund will allow you to receive the $27,000 annuity? Use Appendix C and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
Explanation / Answer
Annual Contribution = $ 11,412.79
Annual Annuity required A = $ 27000
Period of annuity n = 17 years
Interest rate on annuity r = 10% or 0.10
Present Value of annuity at the time of retirement can be calculated as below
Present value of the Annuity = A * [1-1/(1+r)^n]/r
Substituting the values from above
Present Value of Annuity at retirement = $ 27000 * [1-1/(1+0.10)^17]/0.10
= $ 27000 * [1-1/(1.10)^17]/0.10
= $ 27000 * (1-1/5.05447]/0.10
= $ 27000 * (1-0.19784467)/0.10
= $ 27000 * (0.802155331/0.10)
= $ 27000 * 8.02155331
= $ 216,581.9393 or $ 216,581.94 (rounded off)
An amount of $ 216,581.94 is required at the time of retirement to receive an annual annuity of $ 27000 for 17 years at a rate of return of 10%
Future Value of Annuity FV = $ 216,581.94
Period of annual contribution n= 12 years
Rate of return r = 8% or 0.08
Let P be the annual contribution, then future value of annuity can be calculated as follows
Future Value of annuity = P * [(1+r)^n – 1]/r
216581.94 = P * [(1+0.08)^12 – 1]/0.08
216581.94 = P * [(1.08)^12 – 1]/0.08
216581.94 = P * [2.51817 – 1]/0.08
216581.94 = P * (1.51817/0.08)
216581.94 = P * 18.97712646
P = 216581.94/18.97712646
P = $ 11,412.7889 or $ 11,412.79 (rounded off)
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