Question

Question 5 In planning for your retirement, you would like to withdraw $50,000 per year for 15 years. The first withdrawal will occur 20 years from today. Click here to access the TVM Factor Table Calculator What amount must you invest today if your return is 10% per year? $ Round entry to the nearest dollar. Tolerance is +4. What amount must you invest today if your return is 15% per year? $ Round entry to the nearest dollar. Tolerance is +4.

Answer 1

Part 1 Computation of amount to be invested today if the rate of return is 10%p.a.

	Step 1
	PV of Annual payments to be received for 15 years after 20 years from now -
			Annual payment	50000
			Annuity factor @ 10% for 15 years	(1-(1+0.1)^(-15))/(0.1) = 7.606
			PV at the begining of 20th years	380303.975
	Step 2
	PV as on date of the PV computed at Step. 1
			PV at the begining of 20th years	380303.9753
			Discount factor	(1/(1+0.1)^19) = 0.16351
			PV	62182.739

Part 2 Computation of amount to be invested today if the rate of return is 15%p.a.

Step 1
PV of Annual payments to be received for 15 years after 20 years from now -
		Annual payment	50000
		Annuity factor @ 10% for 15 years	(1-(1+0.15)^(-15))/(0.15) = 5.8473
		PV at the begining of 20th years	292368.505
Step 2
PV as on date of the PV computed at Step. 1
		PV at the begining of 20th years	292368.505
		Discount factor	(1/(1+0.15)^19) = 0.07026
		PV	20543.3668