You wish to retire in 20 years, at which time you want to have accumulated enough money to receive an annual annuity of $12,000 for 25 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 $12,000 annuity?
We want have an accumulated balance of $12,000 for 25 years after retirement. During the retirement period return, can be earned of 8% and after retirement it will be 10% on the money invested.
It is required to compute the annual contributions to be made to receive the annual balance of $12,000. First, it is required to compute the present value of an annuity during retirement Present value = annuity amount × PVAF(r, n) Where, PVAF means present value annuity factor, r, means rate of return and n, means number of years. PV = A × PVAF (10%, 25 years) = $12,000 × 9.077 = $108,924
To determine the annual deposit into the account earning 8% that is necessary to accumulate $108,924 after 20 years, use the Future Value of an Annuity table: Appendix C A = Future value ÷ FVAF (r, n) A = FVA ÷ FVAF (8%, 20 years) = $108,924 ÷ 45.762 = $2,380.23
Hence, the annual contribution required to be made per year to receive $ 12,000 at the end of 20 years is $2,380.23