Peter and Blair recently reviewed their future retirement income and expense pro

Question

Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in 34 years and anticipate they will need funding for an additional 24 years. They determined that they would have a retirement income of $57,000 in today's dollars, but they would actually need $81,224 in retirement income to meet all of their objectives. Calculate the total amount that Peter and Blair must save if they wish to completely fiund their income shortfall, assuming a 4 percent inflation rate and a return of 6 percent. Click on the table icon to view the FVIF table . Click on the table icon to view the PVIFA table view the FVIF tableCick on the table icon to view the PVIF A table The total amount that Peter and Blair must save if they wish to completely fund their income shortfal assuming a 4 percent inflation rate and a return of 6 percent is S. (Round to the nearest cent.)

Explanation / Answer

Additional income required=81224-57000=24224

They would need after taking into account inflation 24224*(1.04)35 in year 35 ,24224*(1.04)36in year 36,......,24224*(1.04)58 in year 58 ,they require at t=0 yrs  total present value of above cash flows = 24224*(1.04/1.06)35+24224*(1.04/1.06)36+.....24224*(1.04/1.06)58 = 24224*(1.04/1.06)35(1+(1.04/1.06)1+.....+(1.04/1.06)23)

total present value = 24224*(1.04/1.06)35* (1-(1.04/1.06)24)/(1-(1.04/1.06))

total present value at t=0,= 24224*9.984067=241854.04

Let A be the annual savings by them for 34 years,r=6%

A=(total present value*r)/(1-(1/1+r)34) = (241854.04*.06)/(1-(1/1.06)34) =16832.66

Thus Peter and Blair must save total $16832.66 per year to completely fund their income shortfall.

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