Question

Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in 30 years and anticipate they will need funding for an additional 22 years. They determined that they would have a retirement income of $54,000 in​ today's dollars, but they would actually need ​$78,244 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 4 percent inflation rate and a return of 12 percent.

Answer 1

Step 1

Years to Retire = 30 years

Additional funds required in today's time = $24,244

Value of these additional funds after 30 years = $24,244*(1+4%)^30 = $78,633

Step 2

Additional Income required at retirement = $78,633

Retirement Period = 22 years

Rate of return on corpus = 12%

Inflation rate = 4%

Inflation adjusted rate of return = ((1+12%)/(1+4%))-1 = 7.69%

PV (at the time of retirement, not today) of Corpus required:

where,

• P = $78,633
• r = 7.69%
• n = 22 years

Putting all the values, we get:

PV (at the time of retirement, not today) of Corpus required = $822,171.52

Thus, the total amount that Peter and Blair must save if they wish to completely fund their income​ shortfall is $822,171.52