Question

(a) You have just started a new company to deliver mail and parcels to rural communities. At the moment, other companies either do not provide a service or are exceptionally expensive. The new company requires initial investment to purchase a fleet of 20medium-size vans. These cost £20,000 each and each one requires a down payment of 20 per cent. Your business plan anticipates the vans being fully paid off after 6 years and you wish to make monthly payments on the vans starting a month from now. The APR of the loan is 9.6 per cent. What are the monthly payments?
(b) After 4 years, you are approached by another firm who wishes to buy the postal company. You wish to pay off the van loan completely and approach your bank for details. They have indicated that any early completion of your loan will incur a 1 per cent penalty. You have just paid an instalment and have 24 payments left (next payment in a month). How much will you need to pay the bank today to cancel the loan?

Answer 1

a)
Loan Amount, PV = Number of Vans x Cost per Van x (1 - Down Payment %)
                                = 20 x 20,000 x (1 - 0.2)
                               = 320,000

 

Number of Months, n = Years x 12 = 6 x 12 = 72

Monthly Rate, r = APR / 12 = 9.6% / 12 = 0.8%

Monthly Payment = PV x r / [1 - (1 + r)-n]
                                 = 320,000 x 0.008 / [1 - (1 + 0.008)-72]
                                 = 5,863.92

 

b)
With 24 payments left, n = 24
Monthly Payment, P = 5,863.92
Loan Balance = P x [1 - (1 + r)-n] / r
                         = 5,863.92 x [1 - (1 + 0.008)-24] / 0.008
                         = 127,586.09

 

Penalty = 1% x Loan Balance = 0.01 x 127,586.09 = 1,275.86
Total Amount Needed to be Paid = Loan Balance + Penalty
                                                            = 127,586.09 + 1,275.86 

                                                            = 128,861.95

a. Monthly Payment = 5,863.92

b. Total Amount Needed to be Paid = 128,861.95