Question

In: Finance

You are trying to decide whether to keep your current car or buy a new car....

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 $400 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 $350 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 5% APR (compounded monthly), which alternative is cheaper in present value terms and by how much?

Group of answer choices

keep existing car saves $22,608

get new car, saves $24,515

keep existing car saves $24,450

keep existing car saves $23,286

Solutions

Expert Solution

Present value of keeping existing car = present value of monthly payments

Present value of monthly payments is calculated using PMT function in Excel :

rate = 5% / 12 (converting annual rate into monthly rate)

nper = 120 (10 years with 12 monthly payments each year = 10 * 12 = 120)

pmt = -400 (monthly payment)

PV is calculated to be $37,713

Present value of new car = present value of monthly payments + immediate payment

Present value of monthly payments is calculated using PMT function in Excel :

rate = 5% / 12 (converting annual rate into monthly rate)

nper = 120 (10 years with 12 monthly payments each year = 10 * 12 = 120)

pmt = -350 (monthly payment)

PV is calculated to be $32,998

Present value of new car =  $32,998 + $28,000 = $60,998

Amount saved by keeping existing car = $60,998 - $37,713 = $23,286

jeff jeffy answered 3 months ago
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