Lecture Notes: Compound Interest

Introduction

• Speaker: Quinn, Math Professor at Brauer College.
• Topic: How to calculate compound interest using a calculator.

Simple vs Compound Interest

• Simple Interest: Calculated only on the principal.
• Compound Interest: Calculated on principal plus any previously earned interest.

Compounding Periods

• Annual: Interest is credited once per year.
• Semi-Annual: Twice per year.
• Quarterly: Four times per year.
• Monthly: Twelve times per year.
• Daily: 365 times per year.
• Effect: Exponential growth as interest is added to interest.

Calculation of Compound Interest

• Formula: ( a = p \times \left(1 + \frac{r}{m}\right)^n )
  • a: Final amount in the account.
  • p: Principal or initial amount.
  • r: Annual interest rate.
  • m: Number of compounding periods per year.
  • n: Total number of compounding periods (( m \times t )).
• Operation Order:
  1. Division inside parentheses.
  2. Addition inside parentheses.
  3. Apply exponentiation.
  4. Multiply by ( p ).

Example Calculation

• Initial Deposit: $8,560
• Interest Rate: 4% compounded quarterly for 8 years.
• Values:
  • ( p = 8,560 )
  • ( r = 0.04 )
  • ( m = 4 )
  • ( n = 32 )
• Calculation Steps:
  1. Divide 0.04 by 4.
  2. Add the result to 1.
  3. Raise to the 32nd power.
  4. Multiply by 8,560.
• Result: $11,769.49

Present Value Formula

• Used when the present value is unknown.
• Example Problem: Find present value for $18,000 in 20 years at 5%, compounded monthly.
  • ( a = 18,000 )
  • ( r = 0.05 )
  • ( m = 12 )
  • ( n = 240 )
• Calculation Steps:
  1. Divide 0.05 by 12.
  2. Add to 1.
  3. Raise to 240th power.
  4. Use reciprocal and multiply by 18,000.

Practice Problems

• Multiple scenarios calculated using the formulas.
  • Emphasis on correct operation order and using calculator effectively.
  • Importance of not rounding intermediate steps.

Conclusion

• Tips:
  • Use available resources like eBooks or tutors.
  • Practice solving examples on your own.