Answer: Benjamin would save $11,720.48 over 6 years if he purchases the car instead of leasing it.
Explanation:
To calculate the cost of the car if Benjamin purchases it, we can use the loan amortization formula. The formula for calculating the monthly payment of a loan is:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P = the monthly payment
r = the monthly interest rate (which is the annual interest rate divided by 12)
A = the loan amount
n = the total number of payments
For Benjamin's loan, the loan amount is $30,000, the interest rate is 5.25%, and the loan is for 6 years, or 72 months. Plugging these values into the formula, we get:
r = 0.0525 / 12 = 0.004375
A = $30,000
n = 72
P = (0.004375 * $30,000) / (1 - (1 + 0.004375)^(-72)) = $484.64
Therefore, Benjamin's monthly payment for the car loan is $484.64.
If Benjamin chooses to lease the car instead, he will pay $600 per month for 72 months, plus a $2,500 down payment. Therefore, the total cost of leasing the car is:
Total cost = ($600 * 72) + $2,500 = $45,700
To calculate how much money Benjamin saves by purchasing the car instead of leasing it, we can subtract the total cost of the car loan from the total cost of the lease:
Savings = Total cost of lease - Total cost of car loan
Savings = $45,700 - ($484.64 * 72)
Savings = $11,720.48