Question

Aiisha intends to retire in 11 years and would like to receive ​$670 every six months for 12 years starting on the date of her retirement. How much must Aiisha deposit in an account today if interest is 5 % compounded semi-annually?

Answer 1

Deposit amount today is $ 6,960.47

Step-1:Present Value of semi annual withdrawal
Present Value	=-pv(rate,nper,pmt,fv)
	= $11,982.94
Where,
rate	=	5%/2	=	0.025
nper	=	12*2	=	24
pmt			=	670.00
fv			=	0
Step-2:Present value of deposit amount
Present Value	=-pv(rate,nper,pmt,fv)
	=$ 6,960.47
Where,
rate	=	5%/2	=	0.025
nper	=	11*2	=	22
pmt			=	0
fv			=	11,982.94
Note:
Assuming first wihdrawal is made at the end of six month from the date of retirement.