Question

In: Finance

You plan to retire in 20 years. You would like to maintain your current level of...

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?

Solutions

Expert Solution

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   

  

  


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