Question

Suppose that you have the option to buy the car with a 3 year car loan or lease the car during the same period of time. The 3 year lease option will require a $3,000 down payment and monthly payments of $350. If the salvage value of the new vehicle after 3 years is $5,000 and you can invest at a rate of return of 4%, what is your best option? (Ignore your old vehicle.)

Answer 1

Missing Question Data:

The question was missing the total amount of loan taken. I have found the question online and the missing data is added below.

Explanation:

DATA:

Car Loan = $15000

Interest Rate (annual) = 7% = 0.07

Interest Rate (monthly) = 0.07/12 = 0.00583

Loan Life = 3 years

Period (monthly) = 3*12 = 36

Investment Rate (annual) = 4% = 0.04

Investment Rate (monthly) = 0.04/12 = 0.00333

Salvage value after 3 years (PV of Salvage Value) = $5000

Lease Down Payment = $3000

Lease Monthly Payment = $350

First, we consider the option of Buying on Loan

Car Loan - Salvage Value(PV) = 15000-5000

Car Loan - Salvage Value(PV) = $10000

For the option of Leasing the Car

Sum of monthly lease payments for the total period will be,

Sum of Installments (FV) = 350 * 12 = $12600

We know that,

$PV\;=\;\frac{FV}{(1\;+\;r)^{n}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(here\;n\;=\;4\%\;=\;0.00333)$

Sum of Installments (PV) = $\frac{12600}{(1\;+\;0.00333)^{36}}$

Sum of Installments (PV) = $11178.76

Total Lease Payment = Down Payment + Sum of Installments (PV)

Total Lease Payment = $3000 + $ 11178.76

Total Lease Payment = $14178.76

As we can see that total investment for Loan option is lower than that of Lease option, hence taking Loan is the best choice.