After deciding to acquire a new car, you can either lease the car or purchase it with a two-year loan. The car you want costs $33,000. The dealer has a leasing arrangement where you pay $95 today and $495 per month for the next two years. If you purchase the car, you will pay it off in monthly payments over the next two years at an APR of 5 percent. You believe that you will be able to sell the car for $21,000 in two years. What break-even resale price in two years would make you indifferent between buying and leasing?

$33467.03

Explanation:

Given: we are given that $33000 is the cost of the car that’s on sale if the person wants a cash option.

Leasing option of $495 per month for the next two years with an immediate payment of $95 as a balloon payment for the vehicle.

The person will sell the vehicle for $21000 after 2 years from now.

We need to calculate the breakeven price to sell the vehicle after two years if the person sold the car on either option.

Therefore we will use the future value annuity formula to calculate how much would yield on the lease payments of $495 after two years first.

Where Fv is the future value that will yield from the payments.

P is the periodic payment which is $495 per month.

r is the interest per period so in this case it is 5%/12 as the 5% is on an annual basis and the individual will make monthly payments.

n is the number of payments made and in this case it is 24 payments because $495 is paid monthly for 2 years.

Now we insert the values on the formula above

 Fv = $495 [((1+ (5%/12) ^24)-1)/ (5%/12)]   then compute on a calculator and get the answer

Fv = $12467.03 + $95 we add $95 to the solution because the customer must pay it as a deposit if they choose the lease option.

The value the customer must sell the car for to break even for both options in two years’ time is the sum of $21000 which the customer sells the car for in two years’ time plus the above future value for the lease repayments, so $21000+ $12467.03 =$33467.03 .  

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