Section 4.2: Borrowing - How Much Car Can You Afford?

Welcome to the exciting world of personal finance! In this section, we'll explore the ins and outs of borrowing, specifically focusing on installment loans and mortgages. Understanding these concepts is crucial for making informed decisions about your financial future. Let's get started!

Key Concepts:

  • Installment Loans: Borrowing money for a fixed period, repaid with regular payments that include both principal and interest.
  • Monthly Payment Formula: This formula helps you calculate your monthly payments on a fixed-rate loan. The formula is: $$Monthly Payment = \frac{Amount Borrowed \times r(1 + r)^t}{((1 + r)^t - 1)}$$ where $t$ is the term in months, and $r = APR/12$ is the monthly rate as a decimal.
  • Amortization Schedule: A table showing how each payment is allocated to interest and principal, and the remaining balance.
  • Mortgage Options: Understanding the difference between fixed-rate and adjustable-rate mortgages (ARMs).

Example: College Loan

Let's say you need to borrow $5,000 for college, and you get a loan at an APR of 6% to be paid off in monthly installments over three years. Let's calculate the monthly payment.

First, we need to find the monthly rate, $r$:

$$r = \frac{APR}{12} = \frac{0.06}{12} = 0.005$$

Next, we need to determine the number of months, $t$:

$$t = 3 \times 12 = 36$$

Now, we can plug these values into the monthly payment formula:

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

So, your monthly payment would be $152.11. You can also calculate the amount you can borrow, given a payment you can afford. The formula is: $$Amount Borrowed = \frac{Monthly Payment \times ((1+r)^t - 1)}{(r \times (1 + r)^t)}$$

Section 4.4: Credit Cards - Paying Off Consumer Debt

Credit cards can be powerful tools, but understanding how they work is essential to avoid debt traps. Let's explore some key concepts and calculations related to credit cards.

Key Concepts:

  • Finance Charges: The cost of borrowing money on your credit card, calculated based on the APR and balance.
  • Amount Subject to Finance Charges: Calculated by: $Previous Balance – Payment + Purchases$
  • Minimum Payment Balance Formula: This formula helps you estimate your balance after making only minimum payments for a certain period. $$Balance \space after \space t \space payments = Initial \space balance \times [(1+r)(1-m)]^t$$ where $r$ is the monthly interest rate (APR/12), and $m$ is the minimum monthly payment as a percent of the balance.

Example: Credit Card Balance

Suppose you have a Visa card with an APR of 22.8%. Your previous statement showed a balance of $500. You made a payment of $200 and then bought $400 worth of clothes. Let's find your new balance.

First, calculate the amount subject to finance charges:

$$Amount = $500 - $200 + $400 = $700$$

Next, calculate the finance charge:

$$Finance Charge = \frac{0.228}{12} \times $700 = $13.30$$

Finally, calculate the new balance:

$$New Balance = $700 + $13.30 = $713.30$$

Understanding these calculations empowers you to manage your credit card debt effectively. Keep practicing, and you'll be a financial whiz in no time!