Simple Interest vs. Compound Interest: What's the Difference?

Overview

• Interest Definition: Money paid for borrowing money, calculated as a percentage of the loan amount or deposit.
• Simple vs. Compound Interest:
  • Simple Interest: Paid annually as a percentage of the principal.
  • Compound Interest: Calculated periodically, with interest added to the principal, earning interest itself.

Key Takeaways

• Interest: Cost of borrowing money, expressed as a percentage.
• Simple Interest: Annual percentage based on the principal amount.
• Compound Interest: Based on the principal plus accumulated interest.
• Daily Compounding: Increases interest paid slightly each day.

Simple Interest

• Definition: Annual percentage of a loan paid in addition to the principal.
• Calculation Formula: [ \text{Simple Interest} = P \times r \times n ]
  • ( P ): Principal amount
  • ( r ): Annual interest rate (as a decimal)
  • ( n ): Term of the loan (in years)

Example

• Scenario: Student loan of $18,000 at 6% annual interest for 3 years.
• Interest Calculation:
  • Annual: $18,000 x 0.06 = $1,080
  • Total for 3 years: $1,080 x 3 = $3,240
• Total Repayment: Principal + Interest = $18,000 + $3,240 = $21,240

Compound Interest

• Definition: Interest earned on both the principal and previously earned interest.
• Calculation Formula: [ \text{Compound Interest} = P \times (1 + r)^t - P ]
  • ( P ): Principal amount
  • ( r ): Annual interest rate
  • ( t ): Number of years interest is applied

Example

• Scenario: $100 principal, 10% interest rate, 2 years.
• Calculation: [ 100 \times (1 + 0.10)^2 - 100 = 21 ]
  • Total interest earned = $21

Additional Examples

Simple Interest

• Example 1: $5,000 in a 1-year CD at 3% interest earns $150.
• Example 2: 4-month CD with $5,000 at 3% annual rate earns $50.
• Example 3: Borrow $500,000 at 5% for 3 years, paying $75,000 total interest.

Compound Interest

• Example 4: $500,000 loan at 5% compounded annually for 3 years:
  • Year 1: $25,000
  • Year 2: $26,250
  • Year 3: $27,562.50
  • Total Interest: $78,812.50

Comparison: Which is Better?

• Compound Interest: Better for savings; earns more over time.
• Simple Interest: Preferable for borrowers; less costly over time.

Benefits of Compound Interest for Teens

• Youth Advantage: Starting early increases compounded growth.

The Rule of 72

• Purpose: Estimates time to double an investment at a fixed interest rate.
• Calculation: Divide 72 by the interest rate (e.g., 72/4 = 18 years).

Conclusion

• Savings: Compound interest benefits long-term savings.
• Loans: Pay off loans quickly to minimize compound interest costs.
• Understanding these concepts aids financial decision-making.