Question

solve. Liam borrowed \(\$ 25,200\) from his parents to pay for college. After graduation, he will pay off the loan by making equal monthly payments for six years. How much will each payment be?

Short answer

Answer: Liam will need to pay 350 dollars each month.

Step-by-step solution

Find the total number of months in six years.

There are 12 months in a year. To find the number of months in six years, we simply multiply the number of years by the number of months in a year: 6 years × 12 months/year = 72 months

Calculate the monthly payment.

Now that we know the loan will be paid off in 72 months, we can find out the amount to be paid each month. To do this, we simply divide the total loan amount by the number of months: Total loan amount / Number of months = Monthly payment \(25,200 / 72 = \)350$

Determine the result.

Based on the calculations, Liam will need to pay \(350 each month for 72 months to pay off the total loan amount of \)25,200.

Key concepts

Loan Amortization

Understanding loan amortization is essential when managing personal finances, particularly with large debts like student loans or mortgages. Loan amortization is the process of paying off a loan with regular payments over time. Each payment is divided between the interest costs and reducing the principal amount, which is the original sum borrowed.

At the beginning of the loan term, a larger portion of the payment goes toward interest. Over time, as the principal decreases, more of the payment goes towards paying down the principal. This is because the interest is recalculated on the remaining principal, which gets smaller with each payment. An amortization schedule can help borrowers visualize this process, showing how each payment affects the principal and interest over the loan term.

A very basic example of amortization is repaying a simple interest loan, like in Liam's case, where equal payments are made throughout the term. While simple interest loans are not always fully amortizing (meaning they don't always consider interest cost changes over time), they provide a fundamental understanding of how regular payments reduce a debt.

Monthly Payments Calculation

When dealing with loans, it's crucial to know how to calculate monthly payments, as this affects budgeting and financial planning. To calculate monthly payments for a loan, you typically need to know the total loan amount, the interest rate (if any), and the length of the loan term.

In the case provided, the interest rate is not mentioned, implying a simple interest loan with no interest charged, which simplifies the calculation process. The monthly payment amount is determined by dividing the total loan amount by the total number of payments or months over which the loan will be repaid. However, in real-life scenarios involving interest, this calculation would be more complex and involve additional arithmetic to account for the accruing interest with each payment.

To ensure accuracy and ease of understanding when explaining these calculations, using clear examples and breaking down the formula into understandable parts can improve students' grasp of such financial concepts.

Basic Arithmetic Operations

Grasping basic arithmetic operations is vital for not only solving math problems but also for practical applications like loan calculations. These operations include addition, subtraction, multiplication, and division, and form the building blocks for more advanced math concepts.

In Liam's scenario, multiplication helps determine the total number of payments (6 years × 12 months/year), and division helps calculate each monthly payment (Total loan amount / Number of months). These operations are routinely used in financial calculations to plan and manage loans and investments.

To facilitate a better understanding, it's beneficial to connect these arithmetic operations with real-world examples, such as budgeting or calculating expenses. When students see the relevance and application of math to everyday activities, they are more likely to engage and absorb the material effectively.