You are going to pay cash for a new car and are trying to decide what kind of ca
ID: 1095327 • Letter: Y
Question
You are going to pay cash for a new car and are trying to decide what kind of car to buy. Presently your cash is in a money market account that earns 5% interest. Gas mileage is important to you, but only if it saves you money. Brand A runs on regular unleaded fuel and gets 20 miles per gallon (mpg). Brand B runs on diesel and gets 40 mpg. You will keep your car for 5 years. You will drive your car 10,000 miles per year. You assume regular gas will remain $3 per gallon and the diesel will remain $4 per gallon. Round all answers to the nearest whole number.
To buy one year
Explanation / Answer
cost of one year worth of gasfor brand A = 10000/20 * 3 = 1500
cost of one year worth of gasfor brand B = 10000/40 * 4 =1000
The present value of the gas savings at the end of year 1 for brand A
= 1500/1.05 = 1428.57
The present value of the gas savings at the end of year 1 for brand B
= 1000/1.05 = 952.38
The present value of the gas savings at the end of year 2 for brand A
= 1500/1.05^2 = 1360.54
The present value of the gas savings at the end of year2 for brand B
=1000/1.05^2 = 907.03
The present value of the gas savings across the entire 5 years for brand A
= 1500 * [1-(1.05)^-5]/0.05 = 6494.22
The present value of the gas savings across the entire 5 years for brand B
= 1000 * [1-(1.05)^-5]/0.05 = 4329.48
Based on the gas savings across the 5 year period, you are willing to pay up to more for the diesel car in comparison to the regular car
= 6494.22 - 4329.48
= 2164.74
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