Recursion and Financial Modelling Problem Solving Task Practice SAC

1. Ben is a mobile mechanic. He uses a van to travel to his customers to repair their cars. The value of Ben's van is depreciated using the flat rate method of depreciation. The value of Ben's Van is worth $75000 - $90000 The value of Ben's van, depreciated by a flat rate of 12% - 16% of the purchase price per annum. Cost of van chosen: p.a.......... .$80,000. Interest rate chosen: ....14% a) By how many dollars is the value of the van depreciated each year? Finding D (common difference/ constant) Depreciation=0.14×80,000=11,200 The van is depreciated by $11,200 per year b) Write down a recurrence relation, in terms of Vo, Vn+1 and Vn, that could be used to model the value of the van using this flat rate depreciation. Vn+1 = Vn – 11,200; V = 80,000 c) Using Recursion calculate the value of the van for the first two years. Vo = 80,000 V1 = ...80,000.......- ...11200.......... = 68800 V2 =......68800....... -......11200.. = ...57600