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Wize University Introduction to Finance Textbook > Time Value of Money

Effective Periodic Rate

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Effective Periodic Rates

  • APR must be converted to the appropriate effective periodic rate before cash flow valuation is performed.
  • An effective periodic rate is a rate that corresponds with the frequency of the payments.
  • For example, if payments occur monthly, an effective monthly rate is required to perform time value operations.

Where:
m = number of compounding periods per year
f = number of payments per year (periodicity desired)


Wize Tip
If m and f are the same, you can quickly find the periodic rate by simply dividing the APR.

For Example: 6% interest compounded monthly and paid monthly, the periodic rate is 6% / 12 = 0.5%

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Converting Effective Rates

Useful when you have an effective period rate and wish to find an equivalent rate with a different periodicity.
For example: converting an effective quarterly rate to an effective monthly rate.




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Example: Effective Periodic Rate

What is the effective quarterly rate of an APR of 12%, compounded monthly?

Practice: Effective Periodic Rate

You are planning on borrowing money to buy a new TV. The TV costs $1,200 and the store is offering you a financing of 5% APR compounded semi-annually (twice per year). You will make monthly payments on this loan, what is the effective monthly rate you would need to calculate your monthly payment?


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Example: Effective-to-Effective

Convert a 2% effective quarterly rate to an effective monthly rate.

Practice: Effective-to-Effective

Convert a 3.5% effective semi-annual rate to an effective four-year rate. Round your final answer to 2 decimal places.
Effective four-year rate
%
Extra Practice
What is the effective semi-annual rate of 5% APR compounded every 2 years?
For each of the following scenarios, select which rate would be the most appropriate.
Match the symbol with the correct definition
What is the discount rate in the following scenario?
You plan on retiring in 40 years and would like to save enough money so that you can pay yourself one million dollars per year upon retiring. Your retirement account is expected to earn 9% compounded quarterly.
Round your final answer to 4 decimal places
What is the discount rate in the following scenario?
You borrowed $70,000 to buy a car and will make bi-weekly payments for 4 years. The interest rate charged by the bank is 12% compounded semi-annually.
Round your final answer to 4 decimal places
What is the discount rate in the following scenario?
Karla is saving up for retirement and will put aside $100 per month into an account earning 8% compounded weekly.
Round your final answer to 4 decimal places.
What is the effective monthly rate of 18% APR compounded weekly?
Convert a 8.4% effective quarterly rate to an effective semi-annual rate.
Which of the following provides the highest annual return?
What is the effective quarterly rate of 15% interest compounded every 5 years?
You have a credit card with an APR of 15% compounded monthly and weekly payments. What is the effective periodic rate for each payment period?
You have a loan with an APR of 10% and monthly payments. What is the effective periodic rate for each payment period?