Jim's1998 minivan only averages 20 miles per gallon. He has found a somewhat newer vehicle that averages 26 mpg. He can sell his current minivan for $2800 and purchase the newer vehicle for $4,000. A) Assuming cost of gasoline at $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. B) Considering

Miles - X

Jim sells his minivan for $2800

Buys new vehicle for $4000, in order to buy this new vehicle, $1200 is needed additionally. So he needs to recover this cost.

If he drives with old minivan then his expense is 4 * (X/20)

If he drives with newer vehicle, his expense is and with newer 4 * (X/26)

So savings per year = 4X/20-4X/26=3X/65

To recover the additional cost with an interest of 6%:

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)

1200 = 2.673*3x/65

1200=0.1233x

x=1200/0.1233

x=9732.36 miles per year

So the answer is 9732 miles