Question

Q. Currently Nathan deposits $300 at the end of each month into an IRA and his company will match 40% of his deposit amount. He will retire in 45 years. Assuming his account will earn 8.5% interest rate (APR), how much he can withdraw monthly after his retirement after-tax basis? (Assume he will live for another 25 years after retirement, his average tax rate will be 20%, and his deposit amount will remain constant).

Q. The Purple Pillow is a bed-and-breakfast. This establishment spent $238,700 to refurbish an old mansion and create the current facility. They borrowed 70 percent of the refurbishment cost at 9 percent interest for 15 years. What is the amount of each monthly payment?

Q. Mary and Peter are birthday buddy and just turned 42. Today, Mary told Peter that she started her retirement saving exactly twenty years ago, $200 a month. Peter did not prepare his retirement at all and decided to start his first saving today. Both plan to retire their 67th birthday. Since Mary started 20 years earlier than Peter and both have 25 years to save in the future before their retirement, Peter decided to deposit three times more than Mary per month to catch up. Assume both accounts earn 9.5% per year. Please find who will have how much more when they retire? Mary will not change her retirement saving amount. To have equal amount as Mary’s retirement account at age 67, how much Peter should deposit monthly?

Answer 1

		Monthly Investment Amt is 300+40% of company i.e. 420/-
		Effective Interest Rate=8.5%-20%=6.8%
Answer 1		Perodic Investment		420
		Monthly Rate Of Interest		(6.8/12)
				0.57
		n		540
		Fv	Fv(rate,Nper,Pmt,pv,0)
		Fv		1512441
	Withdrawl of monthly Amt.	Pv=Fv*PVIFA(PIR,n)
		Pv=1512441
		PVIF=Present Value Interest Factor For An Annuiuty at PIR rate for 25Years
		PIR=0.57%
		n=No. Of Periods=300
		Fv=10536
	So Monthly 10536/- Can be withdrawn.
Answer 2	Calculation of monthly payment:
	Amt borrowed:	167090/-
	Withdrawl of monthly Amt.	Pv=Fv*PVIFA(PIR,n)
		Pv=167090
		PVIF=Present Value Interest Factor For An Annuiuty at PIR rate for 15Years
		PIR=0.75%
		n=No. Of Periods=135
		Fv=1973
	Monthly Payment is	1973/-
Answer 3
		Calculation of amt that both would have:
			Marry		Peter
Step1.			At 42 yrs age	At 67 Yrs Age	At 67 Yrs Age
	Perodic Investment		200	200	600
	Monthly Rate Of Interest		(9.5%/12)	(9.5%/12)	(9.5%/12)
			0.79	0.79	0.79
	n		240	540	300
	Fv	Fv(rate,Nper,Pmt,pv,0)
	Fv		142020	1748151	728980
		Marry would have 1019171/- more than peter at the time of retirement:
Step 2.
	To achive equal future value as to marry, peter would have to make investment monthly as follows:
	PMT(R,Nper,Pv,Fv,0/1)
	R=Rate of Interest
	Nper=No of Periods
	Pv =Amt set Aside Today
	Fv=Goal To Be Achived
	0=For Investment at yr end
	PMT=1439/-
	Peter would have to make investment 1439/- monthly to catch up marry.