Question

You are trying to decide whether to keep your current car or buy a new car. If you keep your current car you will pay $350 per month (starting next month) on average for maintenance, gas, property tax and insurance. You will make these payments for 10 years. Alternatively, you can buy a new car and pay $28,000 today and $300 per month (starting next month) on average for maintenance, gas, property tax and insurance. You will make these payments for for 10 years. If your investments earn 4% APR (compounded monthly), which alternative is cheaper in present value terms and by how much? get new car, saves $24,395 keep existing car saves $23,061 keep existing car saves $22,390 keep existing car saves $25,215

Answer 1

We can use PV of an Annuity formula to calculate the present value monthly charges on average for maintenance, gas, property tax and insurance

PV = PMT * [1-(1+i) ^-n)]/i

Where PV =?

PMT = Monthly payment = $350 (for current car)

n = N = number of payments = 10 years *12 months =120 month

i = I/Y = interest rate per year = 4%, therefore monthly interest rate is 4%/12 = 0.33% per month

Therefore,

PV = $350* [1- (1+0.33%)^-120]/0.33%

PV = $34,569.56

Therefore the present value of the cost associated with current car = $34,569.56

Alternatively, you can buy a new car and pay $28,000 today and $300 per month (starting next month) on average for maintenance, gas, property tax and insurance for 10 years

Total cost of car = $28,000 + present value of monthly charges on average for maintenance, gas, property tax

We can use PV of an Annuity formula to calculate the present value monthly charges on average for maintenance, gas, property tax and insurance

PV = PMT * [1-(1+i) ^-n)]/i

Where PV =?

PMT = Monthly payment = $300 (for new car)

n = N = number of payments = 10 years *12 months =120 month

i = I/Y = interest rate per year = 4%, therefore monthly interest rate is 4%/12 = 0.33% per month

Therefore,

PV = $300* [1- (1+0.33%)^-120]/0.33%

PV = $29,631.05

Therefore the total cost associated with new car =$28,000 + $29,631.05 = $57,631.05

There cheaper alternative in present value terms is current car; it is cheaper by

$57,631.05 -$34,569.56 = $23,061.49 or $23,061

Therefore correct answer is option: keep existing car saves $23,061