Peter and Blair

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 25 years. They determined that they would have a retirement income of $71,000 in today's dollars, but they would actually need $97,514in 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 2 percent inflation rate and a return of 8 percent.

The total amount that Peter and Blair must save if they wish to completely fund their income shortfall, assuming a 2 percent inflation rate and a return of 8 percent is $ ??????

Answer 1

Final Answer: Peter and Blair must accumulate approximately $658,864.37 by retirement.

We can solve this problem by calculating their retirement income shortfall, adjusting for inflation, and determining how much money they will need to fund that shortfall over 25 years.

Step 1: Calculate the annual income shortfall.

Desired retirement income = $97,514

Expected retirement income = $71,000

Annual shortfall = $97,514 - $71,000

Annual shortfall = $26,514

This means Peter and Blair need an additional $26,514 per year in today's dollars.

Step 2: Adjust the shortfall for 34 years of inflation.

Since inflation is expected to average 2% annually, the amount they will need in retirement will be higher.

Future shortfall = $26,514 x (1.02)^34

Future shortfall = $51,985.36

Therefore, their annual income shortfall will grow to approximately $51,985.36 by retirement.

Step 3: Calculate the amount needed at retirement.

Peter and Blair expect to need retirement income for 25 years.

Their investments will earn 8% annually, while their required withdrawals will increase by 2% annually due to inflation.

We can use the present value of a growing annuity formula:

PV = Payment x [1 - ((1 + g) / (1 + r))^n] / (r - g)

Where:

Payment = $51,985.36

r = 0.08

g = 0.02

n = 25 years

Substituting:

PV = $51,985.36 x [1 - (1.02 / 1.08)^25] / (0.08 - 0.02)

PV = $658,864.37

Final Answer: $658,864.37

Peter and Blair must have approximately $658,864.37 saved when they retire in 34 years to cover their projected retirement income shortfall for 25 years.

This assumes their first withdrawal occurs one year after retirement, subsequent withdrawals increase by 2% annually, and their savings earn an 8% annual return.

The key idea is that we must account for both inflation and investment growth. Inflation increases their future expenses, while investment returns help their retirement savings last longer.