Question

Guy Keehn is dreaming of retiring at the age of 66, 3 years from now. He would like his retirement plan to provide him with $1,800 a month for 30 years (until he is 96). He currently has $109,000 in savings to deposit into a retirement plan that earns 7.2% compounded monthly. What additional amount must Guy deposit at the end of each month for the next 3 years so that he can then receive $1,800 at the end of each month for the following 30 years?

A. $3,527.89 B. $3,549.06 C. $3,245.56 D. $6,313.08

Answer 1

Step 1 :	Amount should have at age of 66
	Present Value Of Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	= $1800[ 1-(1+0.006)^-360 /0.006]
	= $1800[ 1-(1.006)^-360 /0.006]
	= $1800[ (0.8839) ] /0.006
	= $2,65,178.44
Step 2 :	Future value of current savings of $109000 at age 66
	FV= PV*(1+r)^n
	Where,
	FV= Future Value
	PV = Present Value
	r = Interest rate i.e. 8/4 = 2% per quarter
	n= periods in number ( 6 years *4 = 24)
	= $109000*( 1+0.006)^36
	=109000*1.2403
	= $135192.88
Step 3 :	Amount should be collected from annuity at the age 66
	=$265178.44-135192.88
	=$129985.56
Step 4 :	Calculation of additional amount to be deposited at the end of each month
	Future Value of an Ordinary Annuity
	= C*[(1+i)^n-1]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	129985.56= $C[ (1+0.006)^36 -1 /0.006]
	129985.56= C[ (1.006)^36 -1 /0.006]
	129985.56= C[ (1.2403 -1] /0.006]
	C = $3245.56
	Correct Answer =C. $3,245.56