Question

Suppose the risk-free interest rate is 6.3% APR with monthly compounding. If a $1.9 million MRI machine can be leased for seven years for $24,000 per month, what residual value must the lessor recover to break even in a perfect market with no risk? The residual value must be $. (Round to the nearest dollar)

Answer 1

Monthly Rate = 6.3/12=.525%

Number Of months = 7* 12 = 84

Present worth of machine =[PVA .525%,84* Monthly payment ] + [PVF .525%,84*Residual value]

        1,900,000 =[67.78374*24000] + [.64414*RV]

        1,900,000 = 1626809.76 + .64414 RV

        1,900,000 - 1,626,809.76 = .64414 RV

            RV = 273190.24/.64414

                   = $ 424,116.25    (Rounded to 424116)

**Find present value annuity factor [I= .525%,N= 84 ,PMT= 1] and present value factor( I= .525 ,N= 84 ,FV =1 ] using financial calculator