Pregunta
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
compounded rater of
of
What is the EAR of a quarterly compounded rate of
What is the EAR of a semiannually compounded rate of
(Round to two decimal places.)
adding to or withdrawing from the account. Which would you rather have: a daily compounded rate of
compounded rater of
of
What is the EAR of a quarterly compounded rate of
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
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The EAR for a semiannually compounded rate of 9% is 9.20%.
Solución
To calculate the Effective Annual Rate (EAR) for a semiannually compounded rate, you can use the following formula:
Where:
-
is the nominal annual interest rate (as a decimal). -
is the number of compounding periods per year.
Given:
- Nominal Rate (
) = 9% or 0.09 - Compounding Periods (
) = 2 (since it’s semiannual)
Plugging these values into the formula:
Calculating
Subtracting 1:
Therefore, the EAR for a semiannually compounded rate of 9% is 9.20%.
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Simplifique esta solución The Deep Dive
To answer your question on the effective annual rate (EAR) for a semiannually compounded rate of
where
-
-
(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
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
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