Question

You plan to retire in 20 years. You would like to maintain your current level of consumption which is $48,795 per year. You will need to have 23 years of consumption during your retirement. You can earn 5.97% per year (nominal terms) on your investments. In addition, you expect inflation to be 3.64% inflation per year, from now and through your retirement.

How much do you have to invest each year, starting next year, for 7 years, in real terms to just cover your retirement needs?

Answer 1

Level of Consumption = $48,795 p.a Real Rate of Return = Nominal Rate - Inflation Rate = 5.97 - 3.64 = 2.33%

Assuming 20 yrs to retirement ; Investment to start after 1 yr for 7 years; yrs left after inv upto retirement=20-1-7=12

Total Retirement Consumption at Yr 20 : N=23 yrs PMT=$48795 p.a R=2.33%

PV = PMT[(1 - (1 / (1+ i)^n)) / i]

= 48795[(1-(1/(1+0.0233)^23))/0.0233]

PV of Retirement amt at yr 20 = $858624 (approx)

PV of Retirement amt at end of yr 7 : FV = $858624 N = 12 PMT = 0 R=2.33%

= FV/(1+R)^N

= 858624/(1+0.0233)^12

=$650473

Investment required each year(PMT) : FV =$650473 N=7 R=2.33%

FV=PMT(1+i)[((1+i)^N - 1)/i]

PMT = 650473/{(1.0233)[(1.0233^7-1)/0.0233]}

=$84697 p.a