Question

Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in 29 years and anticipate they will need funding for an additional 21 years. They determined that they would have a retirement income of $62304 in today's dollars, but they would actually need $45000 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 8 percent. 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 8 percent is $______________

Answer 1

Peter and Blair problem:

Given data:

Time to retirement = 29 years; Funding needed time after retirement = 21 years

Retirement income as on date = $62,304

Retirement income needed per year during retirement = $45,000

Inflation rate = 4%, Return = 8%

Let us solve for Income needed at the beginning of retirement to manage for 21 years

Number of years (N) = 21

Interest rate (I/Y) = Nominal interest rate = Inflation + Return (real) = 4%+8% = 12%

Payment at the beginning of each year (PMT) = $45,000

Future value at the end of 21 years (FV) = %0

Let us calculate PV at the beginning of retirement by calculating the Present value of 21 years of income and adding $45,000 needed at the beginning of the retirement year

(Peter and Blair need $45,000 at the beginning of every retirement year which means that at the beginning of 21^st year they need $45,000 and they don’t need any income at the end of 21^st year and hence N becomes only 20)

PV = $45,000 + $45,000/(1+0.12)^1 +$45,000/(1+0.12)^2 + …….. + $45,000/ (1+0.12)^20

Using BA II Plus calculator we can calculate the same like below:

N = 20, I/Y = 12%, PMT = $45,000, FV= $0 è PV1 = -$336124.9631

(Minus symbol is only to represent the negation in equation)

So PV at the beginning of retirement = $45,000 + PV1 = $45,000+$336124.9631 = $381124.9631

Now we need to calculate the savings need to be made by Peter and Blair to have this income at the beginning of their retirement

Present savings = PV = $62,304

Number of years = N = 29 years

Future value (FV) = PV found at the beginning of retirement = $381124.9631

Interest rate (I/Y) = 12%

The equation would look like below:

$62,304 + PMT/(1+0.12)^1 + PMT/(1+0.12)^2 + …… + PMT/(1+0.12)^29 = $381124.9631

Present savings per year needed = PMT = $5990.70839

Using BA II Plus calculator we can calculate the above result like below:

N = 29, I/Y = 12%, PV = -$62,304, FV= $381124.9631 è PMT = $5990.70839

(Minus symbol in PV is only to represent the negation in equation)

So the total amount that Peter and Blair must save if they wish to completely fund their income shortfall, assuming 4% inflation rate and 8% return is $5990.7 per year