Section 4-2: Borrowing and Installment Loans

Let's explore the world of borrowing! This section focuses on installment loans and understanding the factors that influence your monthly payments. We will cover important concepts, including:

  • Installment Loans: Learn about borrowing money for a fixed period with regular payments.
  • Monthly Payment Calculation: Discover how to calculate your monthly payment for a fixed-rate loan using the following formula:

$$ Monthly Payment = \frac{Amount Borrowed \times r(1 + r)^t}{((1 + r)^t - 1)} $$

Where:

  • $r$ = monthly interest rate (APR/12)
  • $t$ = term of the loan in months

Let's try an example! Suppose you need to borrow $5,000 for college with an APR of 6% to be paid off over 3 years. What would your monthly payment be?

First, we calculate the monthly interest rate: $r = \frac{0.06}{12} = 0.005$. Then, we determine the number of months: $t = 3 \times 12 = 36$. Now, we plug the values into the formula:

$$ Monthly Payment = \frac{$5000 \times 0.005(1 + 0.005)^{36}}{((1 + 0.005)^{36} - 1)} = $152.11 $$

  • Amount Borrowed Calculation: Figure out how much you can borrow based on a monthly payment you can afford with the companion monthly payment formula:

$$ Amount Borrowed = \frac{Monthly Payment \times ((1+r)^t - 1)}{(r \times (1 + r)^t)} $$

  • Amortization Table: Understand how each payment is allocated to interest and principal.
  • Mortgage Options: Explore the differences between fixed-rate and adjustable-rate mortgages.

Section 4-4: Credit Cards and Debt Management

This section focuses on understanding credit cards, how finance charges are calculated, and strategies for managing your credit card debt effectively.

  • Credit Card Basics: Get familiar with key terms and concepts related to credit cards.
  • Finance Charge Calculation: Learn how finance charges are calculated on your credit card balance. The amount subject to finance charges is calculated as:

$$ Amount Subject to Finance Charges = Previous Balance - Payment + Purchases $$

The new balance can be found with the following equation:

$$ New Balance = Amount Subject to Finance Charges + Finance Charge $$

  • Minimum Payment Balance: We can calculate the balance after making $t$ minimum payments with the following equation:

$$ Balance \text{ after } t \text{ minimum payments } = Initial Balance \times [(1 + r)(1 - m)]^t $$

Where $r$ is the monthly interest rate and $m$ is the minimum monthly payment as a percent of the balance.

Let's consider an example: Suppose you have a credit card with an APR of 20% and a minimum payment that is 4% of the balance. You have a balance of $250, and you decide to stop charging and make the minimum payment each month. What will be the balance after two years?

In this case, $r = \frac{0.20}{12} = 0.0167$, $m = 0.04$, and $t = 2 \times 12 = 24$. Plugging the values into the formula, we get:

$$ Balance \text{ after } 24 \text{ months } = $250 \times [(1 + 0.0167)(1 - 0.04)]^{24} = $139.55 $$

Loan Calculators

Use these helpful loan calculators to estimate payments and affordability:

Keep practicing, and you'll master these concepts in no time!