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Periodic interest rates. You have a savings account in which you leave the funds for one year without
adding to or withdrawing from the account. Which would you rather have: a daily compounded rate of
, a weekly compounded rate of , a monthly compounded rate of , a quarterly
compounded rater of , a semiannully compounded rate of , or an annually compounded rate
of ?
What is the EAR of a quarterly compounded rate of ?
(Round to two decimal places.)
What is the EAR of a semiannually compounded rate of ?
(Round to two decimal places.)

Ask by Best Kirk. in the United States
Jan 24,2025

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The EAR for a semiannually compounded rate of 9% is 9.20%.

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The Deep Dive

To answer your question on the effective annual rate (EAR) for a semiannually compounded rate of , you can use the following formula:
where is the nominal interest rate, is the number of compounding periods per year, and is the number of years. For your case:
  • (because it compounds semiannually)
Plugging the values into the formula:
Calculating this gives:
To express this as a percentage:
So, the effective annual rate for a semiannually compounded rate is .
Now, about those interest rates you’re considering for your savings—you’d want to pick the option with the highest EAR! The annually compounded seems like a strong contender, but make sure to run the calculations for the others to confirm this!

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