Problem 27 - Thinking Mathematically

Question

You lease a car at \(\$ 605\) per month for 3 years. Estimate the total cost of the lease.

Step-by-Step Solution

Answer

The total cost of the lease is \$21,780.

Step 1: Identify given values

The problem provides the following values: a monthly lease cost of \$605 and a leasing period of 3 years.

Step 2: Convert years to months

There are 12 months in a year. As the car is being leased for 3 years, this amounts to a total of 3 years * 12 months/year = 36 months.

Step 3: Calculate total cost

The total cost of the lease will be the product of the monthly cost and the total number of months. Therefore, it's calculated as \$605/month * 36 months = \$21,780.

Key Concepts

Lease Calculation

When you lease a car, you're essentially paying for the use of the car over a certain period of time. This is different from buying a car because you won't own the car at the end of the lease.
Understanding how to calculate the total cost of a lease is crucial for your budgeting. To find the total lease cost, you need to know:

• The monthly payment amount
• The duration of the lease

Once these values are known, you multiply the monthly payment by the number of months the lease will last. This gives you the total amount you will pay over the lease period.

Monthly Payments

The monthly payment in a lease agreement is how much you pay each month to use the car. This amount is agreed upon before the lease starts and typically stays the same throughout the lease.
"Fixed payments" is key here, as this makes budgeting easier since you'll know exactly what you owe every month. Thus, managing your finances becomes more predictable. For instance, a payment of $605 each month allows you to plan other financial responsibilities around this fixed cost.

Cost Estimation

Estimating the total cost of your lease upfront helps avoid any financial surprises. It involves predicting how much you will end up paying for the entire lease term based on the monthly payments.
In our example, the monthly lease payment of $605, when multiplied by the total lease period in months, gives an estimated total cost. This foresight allows you to compare leasing to other alternatives and make a well-informed decision about car financing.
Knowing the total lease cost upfront can also help in negotiating better terms or deciding if leasing fits your budget.

Basic Arithmetic

In word problems like these, basic arithmetic skills are essential. You need to perform multiplication and possibly other operations to find the solution.
Here, the main task was multiplication, which involves multiplying two numbers: the monthly payment and the total number of months. Such problems often provide straightforward arithmetic, allowing you to build confidence as you solve practical, real-world scenarios.

Time Conversion

Time conversion is crucial when calculating leases, as leases are often discussed in years, but payments are monthly. Hence, converting the period from years to months is an important step.
This conversion is fairly simple: multiply the number of years by 12 (as there are 12 months in a year). For our exercise, leasing a car for 3 years means renting it for 36 months, which was critical to accurately calculating the total lease payments.