Compounding Rates and Present Value

Understanding Compounding Rates and Present Value Calculation

  • Annual Rate vs. Monthly Rate

    • Example given: Monthly rate is 1%.

    • Number of periods = 48.

    • When using present value formulas, the method of compounding is crucial.

    • Annual Compounding:

    • Despite having a monthly rate, we can treat it as an annual case for calculation purposes.

    • Here, 1% is treated as representing an annual rate, with the 48 periods being viewed as 48 months.

    • Result from this calculation yields the same answer as with annual compounding, confirmed as $23,999 at 50%.

  • Monthly Compounding

    • Various compounding options (monthly, quarterly, annually) are available for selection in calculations.

    • When selecting monthly compounding:

    • Incorrect results may occur if the monthly rate is inputted as an annual basis.

    • Calculate monthly period rate:

      • Monthly rate provided in example is 1%

      • Convert it into annual: Multiply by 12, resulting in an annual rate of 12%.

    • Correct Input for Monthly Compounding:

    • Use the annual rate (12%) when selecting monthly compounding for calculation.

    • Ensure the number of periods is still entered as months (48 months).

    • Clicking the present value button with correct inputs will yield a correct result.

  • Key Takeaways

    • Compounding Selection:

    • If monthly compounding is chosen:

      • Input annual percentages, not monthly.

    • Example of correct application would feature 12% as the annual rate when dealing with monthly compounding periods.

    • Annual Compounding Case:

    • Ensure the monthly basis rate (1% provided in example) is correctly plugged in for annual calculations, should the choice be annual compounding.

  • Conclusion

    • Clarification on selection between monthly and annual compounding is critical for achieving accurate calculation results.

    • Emphasis on the necessity to differentiate between the rates based on compounding frequency.

  • Next Topic:

    • Discussion planned on the 'sweepstakes case' in the next session.

  • End of Session

    • Instructor concludes this part of the discussion and urges students to ask questions regarding the learned material.