Libby Company purchased equipment by paying $6,200 cash on the purchase date and agreed to pay $6,200 every six months during the next four years. The first payment is due six months after the purchase date. Libby's incremental borrowing rate is 8%. The liability reported on the balance sheet as of the purchase date, after the initial $6,200 payment was made, is closest to:

(FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided.)

A fix Payment for a specified period of time is called annuity. The discounting of these payment on a specified rate is known as present value of annuity.In this question the monthly payment of $6,200 for 4 years at 8% per year is an annuity.

Formula for Present value of annuity is as follow

PV of annuity = P x [ ( 1- ( 1+ r )^-n ) / r ]

In this question advance payment is also been made which will also included as follow

PV of annuity = P + P x [ ( 1- ( 1+ r )^-n-1 ) / r ]

Where

P = Semiannual payment = $6,200

r = rate of return = 8% / 2 = 4%

n = number of payment = 1+(4 years x 2 payments each year) = 9 payments

PV of annuity = $6,200 + $6,200 x [ ( 1 - ( 1 + 0.04 )^-(9-1) ) / 0.04 ]

PV of annuity = $47,943