Question

Should Jim sell his Minivan? Jim's 1998 minivan is quite functional, but it only averages 20 miles per gallon (mpg). He has found a somewhat newer vehicle (roughly the same functionality) that averages 26 mpg. He can sell his current minivan for $2800 and purchase the newer vehicle for $4,000. Assume a cost of gasoline $4.00 per gallon. How many miles per year must Jim drive if he wants to recover his investment in three years? Assume an interest rate of 6%, zero salvage value for either vehicle after three years, and identical maintenance cost.

Answer 1

Let us assume that Jim needs to drive "x" miles to recover his investment

He sells his minivan for $2800 and buys new vehicle for $4000 therefore additional cost =$1200

This additional Cost needs to be recovered

IF he had drived x miles with old minivan then he would have spent 4*(x/20) on x gallons
and with newer Van eh would spend =4*(x/26) on x gallons

Hence savings per year=4x/20-4x/26=4x(6/520)=3x/65

As we have assumed that Jim needs to drivef x miles per year

Hence we should meet following condition to recover the additional cost

1200=(3x/65)/(1.06)+((3x/65))/(1.06)^2+(3x/65)/(1.06)^3

1200=(3x/65)*((1/1.06)+(1/1.06)^2+(1/1.06)^3)=2.673*3x/65

1200=0.1233x

x=1200/0.1233

x=9732.36 miles per year

Hence he should drive 9732.36 miles per year to recover the additional cost