Question

Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $50,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 3%. He currently has $90,000 saved, and he expects to earn 10% annually on his savings. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below.

Required annuity payments
Retirement income today	$50,000
Years to retirement	10
Years of retirement	25
Inflation rate	3.00%
Savings	$90,000
Rate of return	10.00%
Calculate value of savings in 10 years:			Formulas
Savings at t = 10			#N/A
Calculate value of fixed retirement income in 10 years:
Retirement income at t = 10			#N/A
Calculate value of 25 beginning-of-year retirement payments at t =10:
Retirement payments at t = 10			#N/A
Calculate net amount needed at t = 10:
Value of retirement payments			#N/A
Value of savings			#N/A
Net amount needed			#N/A
Calculate annual savings needed for next 10 years:
Annual savings needed for retirement			#N/A

How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round your intermediate calculations. Round your answer to the nearest cent.

Answer 1

1) Calculate the value of saving in 10 years

This is Simply the compounded value of $90000 @ 10% p.a.

So,

$ 90000 will become $233437 (Rounded off) in 10 years with 10% ROI.

2.) Retirment Income at t=10

Here we need to use ROI 3% inflation because question ask to calculate the value which will have same purchasing power.

So,

So Value of Todays retirement income of $50000 after 10 year willl be $ 67196 (Rounded off)

3) Calculate value of 25 beginning-of-year retirement payments at t =10

Here you need to compute the Present value of the $67196 annual payments for 25 years.

With texas BA 2 calci Put values (Texas BA II easily available online)(Either you can use PV tables)

PMT= -67196, I/Y=10, FV=0,N=24

then Compute PV = 603738.859

Adding 67196 more as there are 25 payments and 1st payment is due on 1st day after 10 year so

Final PV = 603739+67196 = 670935.

$670935 is Value of 25 retirement payments at t=10.

4) Net amount needed at t=10

Value of retirement payments = $670935

Less: value of savings = $(233437)

Net amount needed = $437498

5) Annual payments/savings needed to to accumulate the amount of $437498.

Put values in Texas BA 2 Calculator as

N=10, I/Y= 10,PV=0,FV = 437498

then compute PMT i.e. annual payments = 27450.98

So $27451 annual savings required for next 10 years to meet the retirement goal.