Need some words explaining in addition. John Adams is the CEO of a nursing home

Question

Need some words explaining in addition.

John Adams is the CEO of a nursing home in San Jose. He is now 50 years old and plans to retire in ten years. He expects to live for 25 years after he retires—that is, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $40,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, ten years from today, and he will then get 24 additional annual payments. Inflation is expected to be 5 percent per year for ten years (ignore inflation after John retires); he currently has $100,000 saved up; and he expects to earn a return on his savings of 8 percent per year, annual compounding. To the nearest dollar, how much must he save during each of the next ten years (with deposits being made at the end of each year) to meet his retirement goal? (Hint: The inflation rate 5 percent per year is used only to calculate desired retirement income.)

Explanation / Answer

Solution:

Amount to be withdrawn annually:

Annual withdrawal with inflation impact = 40000*(1+5%)^10 = 65,155.79

Withdrawal for 25 years.

Now, calculate how much balance should he have in account to support 25 withdrawals:

Set financial calculator on BEGIN mode:

Using financial calculator BA II Plus - Input details:

#

I/Y = Rate =

8

PMT =

-$65,155.79

N = Number of years remaining x frequency =

25

FV = Future Value =

$0.00

CPT > PV = Present value to support 25 withdrawals* =

$751,165.30

Now, calculate how much annual payment required to achieve $751,165.40 considering the present funds of $100,000:

Set financial calculator on END mode:

Using financial calculator BA II Plus - Input details:

#

FV = Future Value = Present value to support 25 withdrawals* =

-$751,165.30

PV = Present Value =

$100,000.00

I/Y = Rate / Frequency =

8

N = Number of years x frequency =

10

CPT > PMT = Payment =

$36,949.61

He must save for next 10 years =

$36,949.61

Set financial calculator on BEGIN mode:

Using financial calculator BA II Plus - Input details:

#

I/Y = Rate =

8

PMT =

-$65,155.79

N = Number of years remaining x frequency =

25

FV = Future Value =

$0.00

CPT > PV = Present value to support 25 withdrawals* =

$751,165.30

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