Matemática Financeira Tabela Price

The Tabela Price, also known as the Price Table, is a widely used amortization system in financial mathematics, particularly for loans and mortgages. It’s characterized by fixed installment payments throughout the loan’s duration. While the total payment remains constant, the proportion of the payment allocated to interest versus principal changes over time.

How It Works

At the beginning of the loan, a larger portion of each payment goes towards covering the interest owed. As you progress through the payment schedule, a greater portion of the payment is allocated towards reducing the principal (the initial loan amount). This is because the outstanding principal balance is larger at the start, resulting in higher interest charges. Conversely, as the principal decreases, so does the interest owed, allowing more of the fixed payment to chip away at the principal.

Key Components of a Tabela Price

• Principal (PV): The initial amount borrowed.
• Interest Rate (i): The percentage charged on the outstanding principal, typically expressed as a monthly rate.
• Number of Periods (n): The total number of payment installments (e.g., months).
• Fixed Payment (PMT): The constant amount paid each period. This is calculated using the following formula derived from present value of annuity concepts:
  PMT = PV * [i(1+i)^n] / [(1+i)^n – 1]
• Interest Payment (Interest): The portion of the payment that covers the interest accrued for that period. It’s calculated as:
  Interest = Outstanding Principal * Interest Rate
• Principal Amortization (Principal): The portion of the payment that reduces the outstanding principal balance. It’s calculated as:
  Principal = PMT – Interest
• Outstanding Principal Balance (Balance): The remaining amount owed after each payment. It’s calculated as:
  Balance (new) = Balance (old) – Principal

Constructing a Tabela Price

A Tabela Price is usually presented as a table with columns for the payment number, payment amount, interest portion, principal amortization, and outstanding balance. Each row represents a payment period.

1. Calculate the fixed payment (PMT) using the formula above.
2. For the first period: Calculate the interest payment by multiplying the initial principal by the interest rate. Subtract the interest payment from the fixed payment to find the principal amortization. Subtract the principal amortization from the initial principal to get the new outstanding balance.
3. For subsequent periods: Repeat the process, using the outstanding balance from the previous period to calculate the interest payment for the current period. Continue until the outstanding balance reaches zero (or a negligible amount), indicating the loan is fully repaid.

Advantages and Disadvantages

Advantages:

• Predictability: Fixed payments make budgeting easier.
• Wide Availability: Commonly used for mortgages and other loans.
• Simplicity: Relatively easy to understand compared to other amortization systems.

Disadvantages:

• Higher Interest Paid Early On: You pay more interest at the beginning of the loan term.
• Slower Principal Reduction: Compared to systems where principal payments are higher early on, your principal decreases more slowly.

Conclusion

The Tabela Price provides a structured and predictable way to repay loans. Understanding its mechanics is crucial for borrowers to comprehend how their payments are allocated and how their principal is reduced over time. While the fixed payment offers budgeting convenience, it’s important to be aware of the higher interest payments incurred at the start of the loan term.