Section 4-2: Borrowing - How Much Can You Afford?

In this section, we'll delve into the world of borrowing, focusing on installment loans and mortgages. Understanding these concepts is crucial for making informed financial decisions. Let's start with installment loans:

  • Installment Loans: These loans involve borrowing money for a fixed period, with regular payments to cover the principal and interest. The payment amount depends on the principal, the interest rate (APR), and the loan term.

The monthly payment can be calculated using the following formula:

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

Where:

  • $r = APR/12$ (monthly interest rate as a decimal)
  • $t =$ term in months

Example: Let's say you need to borrow $5,000 for college at an APR of 6%, to be paid off in 3 years. Using the formula, we find:

$r = 0.06/12 = 0.005$ and $t = 3 \times 12 = 36$

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

Therefore, your monthly payment would be $152.11.

We can also determine how much you can borrow given a certain monthly payment. The formula is:

$$ Amount Borrowed = \frac{Monthly Payment \times ((1 + r)^t - 1)}{(r \times (1 + r)^t)} $$
  • Amortization Table: An amortization table shows how each payment is allocated to interest and principal, and the remaining balance. It's a great way to track the progress of your loan repayment and understand how much equity you have in an item you are paying off.
  • Mortgages: Loans specifically for purchasing a home. Key terms include:
    • Fixed-rate mortgage: maintains the same interest rate throughout the loan's life.
    • Adjustable-rate mortgage (ARM): has an interest rate that can change over time.

Section 4-4: Credit Cards - Paying Off Consumer Debt

Credit cards can be useful tools, but it's vital to understand how they work to avoid accumulating debt. Let's examine some key concepts:

  • Amount Subject to Finance Charges: This is the balance upon which interest is calculated. It is calculated as:
$$ Amount Subject to Finance Charges = Previous Balance - Payment + Purchases $$
  • New Balance: Calculated by adding the finance charge to amount subject to finance charge.
$$ New Balance = Amount Subject to Finance Charges + Finance Charge $$

Example: Suppose your Visa card has an APR of 22.8%. Your previous statement showed a balance of $500, and you made a $200 payment, followed by $400 in new purchases. Let's calculate the new balance:

Amount subject to finance charges = $500 - $200 + $400 = $700

Finance charge $= (0.228/12) \times $700 = $13.30

New balance = $700 + $13.30 = $713.30

  • Minimum Payment Balance: Making only the minimum payment can significantly extend the repayment period and increase the total interest paid. The balance after t minimum payments is calculated as:
$$ Balance After t Minimum Payments = Initial Balance \times [(1 + r)(1 - m)]^t $$

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

Remember, understanding these concepts can empower you to make smarter financial decisions. Keep practicing, and you'll be a finance whiz in no time!