Question

Keith wants to buy his first vehicle for $10,000. the dealer will sell it to him over three years at seven percent interest or lease it to him for the same rate over the same period. the vehicle has a residual value of $5,000 at the end of the lease. using the table, which compares lease and purchases monthly payments, if keith has no down payment, calculate how much less his monthly lease payments will be than his monthly purchase payments?

a. $123.34
b. $314.59
c. $125.22
d. $211.34

Answer 1

To calculate how much less Keith's monthly lease payments will be than his monthly purchase payments, we can use the formulas for calculating loan payments and lease payments. The monthly loan payment for the purchase option is $314.59 and the monthly lease payment is $191.25. Therefore, Keith's monthly lease payments will be $123.34 less than his monthly purchase payments.

Step-by-step explanation:

To compare the lease and purchase payments for Keith's vehicle, we can use the formula for calculating monthly loan payments and the formula for calculating lease payments.

For the purchase option, the formula for monthly loan payments is:
Loan amount (PV) = $10,000
Interest rate (r) = 7% per year = 0.07
Number of periods (n) = 3 years = 36 months
Monthly loan payment = PV * (r/12) / (1 - (1 + r/12)^-n)

Using this formula, we can calculate the monthly loan payment for the purchase option, which is $314.59.

For the lease option, the formula for monthly lease payments is:
Lease amount (PV) = $10,000 - $5,000 (residual value) = $5,000
Interest rate (r) = 7% per year = 0.07
Number of periods (n) = 3 years = 36 months
Monthly lease payment = PV * (r/12) / (1 - (1 + r/12)^-n)

Using this formula, we can calculate the monthly lease payment, which is $191.25.

Therefore, Keith's monthly lease payments will be $314.59 - $191.25 = $123.34 less than his monthly purchase payments.

Answer 2

Keith's monthly lease payments will be around $123.34 less than his monthly purchase payments.

Step-by-step explanation:

To calculate how much less Keith's monthly lease payments will be than his monthly purchase payments, we need to compare the two options. Let's start with the monthly purchase payments:

Using the formula for calculating monthly payments on a loan:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

For the purchase option, the loan amount is $10,000, the interest rate is 7% (convert it to 0.07), and the number of payments is 3 years = 36 months. Plugging in these values in the formula gives us:

Monthly Purchase Payment = ($10,000 * 0.07) / (1 - (1 + 0.07)^(-36))

Solving this, the monthly purchase payment is approximately $314.59.

Now let's calculate the monthly lease payment:

Since the residual value of the vehicle at the end of the lease is $5,000, the lease amount is $10,000 - $5,000 = $5,000. Using similar calculations as above, we get the monthly lease payment to be approximately $191 25.

Therefore, the difference between Keith's monthly lease payments and monthly purchase payments is approximately $314.59 - $191.25 = $123.34.