Professor Baker's Math Class: Interest Worksheets (February 4th - February 14th, 2014)

Welcome to a new week of math! Over the next two weeks, we'll be diving into the world of interest. Understanding how interest works is crucial for making informed financial decisions, whether you're saving money or taking out a loan. Let's get started and don't hesitate to ask questions. I'm here to help you succeed!

Here's the breakdown of assignments and key concepts we'll be covering. Remember to check the "Class Notes" link daily for updated notes from each class session.

Key Concepts:

  • Simple Interest: Interest calculated only on the principal amount. The formula is: $I = Prt$, where $I$ is the interest, $P$ is the principal, $r$ is the interest rate (as a decimal), and $t$ is the time (in years).
  • Compound Interest: Interest calculated on the principal and the accumulated interest. This is where your money can really grow! The formula for annual compound interest is: $A = P(1 + r)^t$, where $A$ is the amount after $t$ years. For interest compounded $n$ times per year, the formula is: $A = P(1 + \frac{r}{n})^{nt}$.
  • Maturity Value: The total amount due at the end of a loan, including the principal and the interest. For simple interest loans, Maturity Value (MV) = $P + I$.
  • Present Value: The amount of money you need to invest *today* to reach a specific goal in the future. The formula for present value is: $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$
  • Effective Annual Yield: The simple interest rate that produces the same amount of money in an account at the end of one year as when the account is subjected to compound interest at a stated rate. $Y = (1 + \frac{r}{n})^n - 1$

Homework Assignments

  • Class Notes: This link will be updated daily with the notes for class
  • Homework Packet
  • 02-04: pg 439 # 1-24 all
  • 02-06: Worksheet
  • 02-07: Worksheet
  • 02-10: pg. 439 # 25-32
  • 02-11: pg. 439-440 # 33-40
  • 02-13: pg. 440 # 41-47
  • 02-14: Don't forget your W-2!

Example Problem (Simple Interest): If you deposit $2000 in a savings account that earns 6% simple interest per year, how much interest will you earn after one year?

Solution: Using the formula $I = Prt$, we have $P = 2000$, $r = 0.06$, and $t = 1$. Therefore, $I = 2000 * 0.06 * 1 = $120$. You will earn $120 in interest.

Example Problem (Compound Interest): You deposit $2000 in a savings account that earns 6% interest per year, compounded annually. How much money will you have after 3 years?

Solution: Using the formula $A = P(1 + r)^t$, we have $P = 2000$, $r = 0.06$, and $t = 3$. Therefore, $A = 2000 * (1 + 0.06)^3 = 2000 * (1.06)^3 \approx $2382.03$. You will have approximately $2382.03 in the account after 3 years.

Remember to practice these concepts and reach out if you need any clarification. Good luck with your assignments!