Overview

This topic introduces mathematical tools used in personal finance, including interest, percent change, markups, discounts, and future value. You'll learn to solve problems involving loans, savings, taxes, and investment growth using simple and compound interest formulas.

Key Concepts and Structures

• Percent and Percent Change:
  • Percent = part / whole × 100%
  • Percent change = (new - old) / old × 100%
• Markup and Discount:
  • Markup = cost × (1 + % markup)
  • Discount = price × (1 - % discount)
• Simple Interest: I = Prt
  • P = principal
  • r = rate (decimal)
  • t = time in years
• Compound Interest: A = P(1 + r/n)^{nt}
  • A = amount after interest
  • n = number of times compounded per year
• Continuous Compounding: A = Pe^{rt}
• Future Value: How much an investment will be worth later.
• Present Value: How much needs to be invested now to reach a future amount.
• Effective Annual Rate (EAR): Actual annual return based on compounding. EAR = (1 + r/n)^n - 1

Step-by-Step Example

Problem: Find the amount after 5 years if $1,000 is invested at 6% annual interest compounded monthly.

Step 1: Use compound interest formula:
A = P(1 + r/n)^{nt}

Step 2: Identify values:
P = 1000, r = 0.06, n = 12, t = 5

Step 3: Plug in values:
A = 1000(1 + 0.06/12)^{12×5} = 1000(1.005)^60 ≈ 1348.85

Final Answer: $1,348.85

Quick Tip