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 3131 years and anticipate they will need funding for an additional 2323 years. They determined that they would have a retirement income of $77 comma 00077,000 in today's dollars, but they would actually need $105 comma 356105,356 in retirement income to meet all of their objectives. Calculate the total amount that Peter and Blair must save if they wish to completely fund their income shortfall, assuming a 33 percent inflation rate and a return of 88 percent.

Explanation / Answer

The shortfall = $105356 - $77000 = $28356

This is an inflation adjusted amount, we have to calculate the future value of this amount using the inflation rate of 3% ; Time for funding = 23 years

FV of shortfall = 28356 x (1+ 0.03)^23 = $55963

To get this amount each year for 23 years, we know our return is 8% with 3% inflation. This gives a real return of 4.85% = ((1.08)/(1.03)) – 1.

Now assuming we needed an annuity of $55963 for 23 years at a 4.85% return, we set our PMT = 55963, N = 23, I = 4.85%, and it gives a PV of $765,652 calculated as 55963 x (PVIFA,4.85%, 23). This is the amount we need to have available each year in 23 years.

Therefore, to get this amount, we set the FV = $765,652, N = 23, I = 8%, and calculate the PMT = $9,786 is the payment each year to meet this shortfall.

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