Question

Your local auto store is willing to lease you a new car for $254 a month for 66 months. Payments are due on the first day of each month starting with the day you sign the lease. Using an APR of 8.50% compounded semi-annually, what is the present value of the lease?

Question 1 options:

$12,822

$13,160

$13,497

$13,834

$14,172

Answer 1

$13,497

Step-1:Calculation of monthly interest rate compounding monthly
(1+i)^n		=	(1+i)^n		Where,
(1+0.0425)^1	=	(1+i)^6		Semi annual interest rate	=	8.5%/2	=	0.0425
1.0425		=	(1+i)^6
1.0425	^(1/6)	=	1+i
1.006961		=	1+i
0.006961		=	i
So, Monthly interest rate	=	0.6961%
Step-2:Calculation of present value of lease
Present Value of lease	=-pv(rate,nper,pmt,fv,1)		Where,
	= $ 13,497			rate	=	0.006961062
				nper	=	66
				pmt	=	$                 254
				fv	=	0
Note:
1 is used in the excel formula because cash flows are at the beginning of month.