Lecture on Financial Mathematics: Effective Rate Interest Formula

Presenter

• Zo Li from Bright Young Brains

Topic

• Financial Mathematics: Using the Effective Rate Interest Formula

Key Concepts

• Nominal Rate (I_Norm): The stated interest rate on a loan before taking into account compounding.
  • In the example provided, I_Norm is 13%.
• Compounding Frequency (M): How often the interest is compounded over a period.
  • In the example provided, the interest is compounded monthly, thus M = 12.

Problem Statement

• John purchased a car and received a loan from the bank.
• The loan had a nominal rate of 13% per annum, compounded monthly.
• Objective: Calculate the effective annual interest rate.

Effective Rate Interest Formula

• Formula: Involves converting nominal interest rate to effective interest rate considering the frequency of compounding.

Steps to Solve

1. Identify given values:
   • I_Norm = 13%
   • M = 12 (since compounding is monthly)
2. Convert I_Norm to decimal if necessary:
   • 13% as a decimal is 0.13 or 13/100.
3. Use the effective rate interest formula:
   • Plug in the values for I_Norm and M.
4. Calculation:
   • Compute using a calculator.
   • Write results to four decimal places.
   • Multiply by 100 to convert the result into a percentage.

Conclusion

• Understanding how to apply the effective rate interest formula helps in determining the real cost of borrowing or the real return on investments.

Additional Resources

• View more videos in the playlist for similar problems and solutions.