Question

30. George and Julia anticipate that they will require an annual income of $72,000 (in today's dollars) when they retire 15 years from now. They expect to receive Social Security benefits of $18,000 per year at that time. In calculating their retirement savings need, they are assuming a 3% annual rate of inflation, an 8% after-tax return on investments, and a 25-year retirement period. What is the total amount of retirement fund or capital that George and Julia will require to support their income needs at the beginning of their retirement? (Round your answer to the nearest dollar.) A. $1,412,257 B. $1,203,226 C. $1,261,635 D. $1,356,875

Answer 1

	Inputs:
		Years to retirement	15
		Length of retirement (in years)	25
		Annual interest rate	8%
		Annual Inflation(Assumed)	3%
		Retirement income in todays dollar	$72,000
	Ouputs:
		Inflation Adjusted Return on investment	4.85%	((1+0.08)/(1+0.03))-1
		Retiremet income needed at the time of retirement	$112,174	(72000*(1.03^15)
		Less:Social Security Benefit	$18,000
		Retirement income from Savings	$94,174
		Total amount of retirement fund or Capital needed	$1,412,252	(Using PV Function of excel with Rate=4.85%,Nper=25,Pmt=-94174,Type=1)
		Type=1 , because income is at the beginning of years
		ANSWER:
		A.1412257
		Minor difference is due to approximation in inflation adjusted return
				X fc =PV(H12,H6,-H15,,1) Η Ι Ι Ι Ι Κ Ι ι Ι Μ Ι Ν Ι ο Inputs: Years to retirement Length of retirement (in years) Annual interest rate Annual Inflation Assumed) Retirement income in todays dollar 3% $72,000 Ouputs: Inflation Adjusted Return on investment Retiremet income needed at the time of retirement Less:Social Security Benefit Retirement income from Savings Total amount of retirement fund or Capital needed 4.85% ((1+0.08)/(1+0.03))-1 $112,174 (72000*(1.03415) $18,000 $94,174 $1,412,252 (Using PV Function of excel with Rate=4.85%,Nper=25, Pmt=-94174,Type=1)