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

Answer:

Here in the question it is given tha the income of both of them after retirement would be $57000.

But the income that they want to get after retirement = $87224

Hence a shortfall of $30224 which is needed for 24 years and after 34 years of their retirement.

Given that the inflation rate = 4% an drequired return = 6% so the discount rate should be 10% so that inflation adjusted real return should be 6%.

Now we have to use PV of annuity formula to get the value of $30224 for 24 years at discount rate of 10% This present value would be at the end of 34th year.

Hence

PV = $30224 x PVIFA(10%, 24years) = $30224 x 8.9847 = $271553.57

and now use this value of $271553.57 to calculate pmt on 10% discount rate for 34 yaers:

PMT = $1106.23

So this amount should be invested for 34 years every year to get annuity of $87224 for another 24 years after retirement.

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