After deciding to buy a new car, you can either lease the car or purchase it on a 3-year loan. The car costs $32,000. The lease offer is for $450/month for 36 months, with only $99 due up front. If you buy the car with a 3-year loan, the APR is 7% with monthly compounding. You believe that in 3 years the car will be worth $23,000. Should you buy or lease?
To determine whether you should buy or lease the car, we need to compare the total costs of both options.
First, let's calculate the total cost of leasing the car:
Lease offer: $450/month for 36 months
Total Lease payments: $450/month * 36 months = $16,200
Amount due upfront: $99
Total cost of leasing: $16,200 + $99 = $16,299
Now, let's calculate the total cost of buying the car using a 3-year loan:
Car cost: $32,000
APR: 7%
Monthly compounding
Loan period: 3 years (36 months)
To calculate the monthly payment, we can use the loan payment formula:
Loan Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Principal (car cost)
r = Monthly interest rate (APR/12)
n = Number of months (loan period)
Monthly interest rate (r) = 7% / 12 = 0.5833%
Loan Payment = $32,000 * (0.5833% * (1 + 0.5833%)^36) / ((1 + 0.5833%)^36 - 1)
Using a financial calculator or a spreadsheet, we can calculate the monthly payment:
Loan Payment ≈ $981.12
Total cost of buying the car: $981.12/month * 36 months = $35,320.32
Lastly, let's compare the total cost of leasing ($16,299) with the total cost of buying ($35,320.32).
Since the total cost of leasing is considerably lower than the total cost of buying, it appears to be a more financially advantageous option in this scenario.
However, it's vital to consider other factors such as your personal preferences, mileage requirements, and the potential costs of maintenance and repairs, which are not factored into this analysis.