Assume you plan to put money in an investment at the end of each year for 40 yea

Question

Assume you plan to put money in an investment at the end of each year for 40 years. you plan to increase your annual contribution by 2.50% annually (a growing annuity). In 40 years you plan to use your accumulated savings to buy an annuity that will pay you $100,000 at the end of every year fro 20 years. Use a 10% discount rate to estimate how much your first (year 1) contribution must be in order for you to adequately finance your retirement.

NOTE: Please use financial calculator TVM to calculate the answer.

Explanation / Answer

R=100,000 I=10% Growing annuity=2.5% Pv=R[(1-1/1+i)n/i] Pv=100,000[(1-1/1+.10)/.10]+97,500[(1-1/1+.10)20/.10]+95,063[(1-1/1+.10)19/.10]+92,687[(1-1/1+.10)18/.10]+90,370[(1-1/1+.10)17/.10]+88,111 [(1-1/1+.10)16/.10]+85,909[(1-1/1+.10)15/.10]+83,762[(1-1/1+.10)14/.10]+81,668 [(1-1/1+.10)13/.10]+79,627[(1-1/1+.10)12/.10]+77,637[(1-1/1+.10)11/.10]+75,697[(1-1/1+.10)10/.10]+73805[(1-1/1+.10)9/.10]+71960[(1-1/1+.10)8/.10]+70161[(1-1/1+.10)7/.10]+68407[(1-1/1+.10)6/.10]+66697[(1-1/1+.10)5/.10]+65030[(1-1/1+.10)4/.10]+63405[(1-1/1+.10)3/.10]+61820[(1-1/1+.10)2/.10]+60275[(1-1/1+.10)1/.10] So we have to find out first year contribution =60275[(1-1/1+.10)1/.10] =$54850 Share: by email on facebook on twitter

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