Question

Joe Smith just celebrated his 30th birthday and has decided that he needs to start saving towards retirement. He plans on retiring on his 60th birthday. Through his 30s he plans on saving $500 per month starting one month from his birthday. Through his 40s he plans on saving $1000 per month. Through his 50s he plans on saving $2000 per month. If he can invest these savings in an investment that pays 6% (annually rate) how much money will he have on his 60th birthday.

B) taking the money Joe Smith has on his 60th birthday determine how much he could be paid per month, starting one month after his birthday, if he wishes to receive his annuity until age 90 and the interest rate is 5%.

Answer 1

A)	FV of savings for the 1st 10 year period = 500*(1.005^120-1)*1.005^240/0.005 =	$     2,71,237
	FV of savings for the 2nd 10 year period = 1000*(1.005^120-1)*1.005^120/0.005 =	$     2,98,162
	FV of savings for the 3rd 10 year period = 2000*(1.005^120-1)/0.005 =	$     3,27,759
	Amount available on the 60th birthday =	$     8,97,157
B)	The above amount is the PV of the monthly withdrawals to be made. Using the formula for finding annuity given PV of the annuity, the monthly withdrawals =
	= 897157*0.005*1.005^360/(1.005^360-1) =	$           5,379