Question

The first of twelve semiannual payments of $2500 will be made 6.5 years from today. What is the present value of this deferred annuity using a discount rate of 7.5% compounded semiannually? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

  

Present value

$

Answer 1

Step 1 :	Value of annuity at the end of year 6 from now
	Present Value Of Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	r = Interest rate =7.5%/2 =3.75%
	n=number of period
	= $2500[ 1-(1+0.0375)^-12 /0.0375]
	= $2500[ 1-(1.0375)^-12 /0.0375]
	= $2500[ (0.3571) ] /0.0375
	= $23,806.73
Step 2 :	Value of 23,806.73 today
	PV= FV/(1+r)^n
	Where,
	FV= Future Value
	PV = Present Value
	r = Interest rate =7.5%/2 =3.75%
	n= periods in number =6*2 =12
	= $23806.73/( 1+0.0375)^12
	=23806.73/1.55545
	= $15305.32
	Correct Answer = $15305.32