Comparing Lease and Buy for a Used Vehicle
A student needs a vehicle for 3 years. Option 1 is a lease: $310 per month for 36 months, $2,000 due at signing, and a limit of 20,000 km per year with a $0.15 per km charge beyond that. The student drives about 18,000 km per year, but one year they expect 24,000 km. Option 2 is buying a used car for $14,500 with a 3-year loan at 6.5% annual interest compounded monthly, amortized over 36 monthly payments. The bought car would be worth about $8,000 after 3 years. Insurance is $145 per month either way, and maintenance averages $60 per month for the lease (covered) versus $95 per month for the bought car.
1. Calculate the total 3-year cost of the lease including the excess-kilometre charge in the high-kilometre year, plus insurance and maintenance.
Read the worked answer
Monthly lease payments: 36 × $310 = $11,160. Due at signing: $2,000. Lease subtotal = $13,160.
Excess kilometres: the limit is 20,000 per year. In the high year, 24,000 - 20,000 = 4,000 excess km. Charge = 4,000 × $0.15 = $600. The other two years (18,000 km) are within the limit. Total lease cost = 13,160 + 600 = $13,760.
Insurance: 36 × $145 = $5,220. Maintenance: 36 × $60 = $2,160.
Total 3-year cost = 13,760 + 5,220 + 2,160 = $21,140.
2. Calculate the monthly loan payment for buying, then the total 3-year cost including insurance, maintenance, and resale value.
Read the worked answer
Use the amortization formula: P = L × i / (1 - (1 + i)^(-n)), where L = 14,500, annual rate 6.5% so monthly i = 0.065 / 12 ≈ 0.0054167, and n = 36.
(1 + i)^(-36): first compute (1.0054167)^36. Using logs or repeated multiplication, (1.0054167)^36 ≈ 1.2147, so the reciprocal ≈ 0.8233. Then 1 - 0.8233 = 0.1767.
Payment = 14,500 × 0.0054167 / 0.1767 ≈ 78.54 / 0.1767 ≈ $444.44 per month.
Total payments = 36 × 444.44 ≈ $15,999.84, so interest ≈ $1,500.
Insurance: 36 × 145 = $5,220. Maintenance: 36 × 95 = $3,420. Resale value after 3 years: $8,000 (subtract from cost).
Net 3-year cost = 15,999.84 + 5,220 + 3,420 - 8,000 = $16,639.84.
3. Recommend lease or buy, and explain how the high-kilometre year and resale uncertainty affect the decision.
Read the worked answer
Buying has a net 3-year cost of about $16,640, while leasing costs about $21,140 - buying is cheaper by roughly $4,500 over three years.
The high-kilometre year adds $600 to the lease and could add more if driving increases further; every 1,000 excess km costs $150. Buying has no kilometre penalty, so it is more robust to driving uncertainty.
The main risk in buying is resale value. If the car is worth only $6,000 instead of $8,000, the buy cost rises to about $18,640, still below the lease. The lease would only become competitive if resale fell below about $3,500, which is unlikely for a $14,500 car after 3 years.
Recommendation: buy, because it is cheaper in the expected case and less exposed to kilometre overages, while resale risk does not reverse the comparison.