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 $45,000 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 4%. He currently has $145,000 saved, and he expects to earn 8% 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
Current Age	50
Retirement income today (1st retirement payment same Purchasing power	$45,000
Years to retirement	10
Years of retirement	25
Inflation rate	4.00%
Savings	$145,000
Rate of return	8.00%
Calculate value of savings in 10 years:			Formulas
Savings at t = 10
Calculate value of fixed retirement income in 10 years:
Retirement income at t = 10	$0.00		0
Calculate value of 25 beginning-of-year retirement payments at t =10:
Retirement payments at t = 10	$0.00		$0.00
Calculate net amount needed at t = 10:
Value of retirement payments	$0.00		$0.00
Value of savings			$0.00
Net amount needed	$0.00		$0.00
Calculate annual savings needed for next 10 years:
Annual savings needed for retirement			$0.00

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

Required annuity payments
Retirement income today	$          45,000
Years to retirement	10
Years of retirement	25
Inflation rate	4.00%
Savings	$       1,45,000
Rate of return	8.00%
Calculate value of savings in 10 years:		Formulas
Savings at t = 10	$ 3,13,044.12	= 145000*1.08^10 =
Calculate value of fixed retirement income in 10 years:
Retirement income at t = 10	$     66,610.99	= 45000*1.04^10 =
Calculate value of 25 beginning-of-year retirement payments at t =10:
Retirement payments at t = 10	$ 7,67,942.00	= 66610.99*1.08*(1.08^25-1)/(0.08*1.08^25) =
Calculate net amount needed at t = 10:
Value of retirement payments	$ 7,67,942.00
Value of savings	$ 3,13,044.12
Net amount needed	$ 4,54,897.88
Calculate annual savings needed for next 10 years:
Annual savings needed for retirement	$     31,401.37	=454897.88*0.08/(1.08^10-1) =