Question

• ABC Corp. wishes to invest a fixed sum at 4.65% and withdraw $10,000 at the end of each month for the next three years. How much ABC will need to invest? In other words, what is the present value of an ordinary annuity of $10,000 for 36 periods, discounted at a rate of 4.65%/12 per period?
• Assume that ABC Corp can earn 4.65%, but needs to withdraw $10,000 for 72, not 36 months. How much cash must it now invest to meet its $10,000 / month needs?

Assume that ABC Corp. can only earn 3.5% on its investment. What sum does it now need to invest to meet its $10,000 / month cash needs for 72 months?

Answer 1

Case 1:	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	= $10000[ 1-(1+0.003875)^-36 /0.003875]
	= $10000[ 1-(1.003875)^-36 /0.003875]
	= $10000[ (0.13) ] /0.003875
	= $335,412.81
Casse 2 :	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	= $10000[ 1-(1+0.003875)^-72 /0.003875]
	= $10000[ 1-(1.003875)^-72 /0.003875]
	= $10000[ (0.2431) ] /0.003875
	= $627,231.18
Case 3 :
	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	= $10000[ 1-(1+0.0029166667)^-72 /0.0029166667]
	= $10000[ 1-(1.0029166667)^-72 /0.0029166667]
	= $10000[ (0.1892) ] /0.0029166667
	= $648,575.85