Question

Let the following interest rate 3.80% be considered a nominal interest rate. Given the nominal rate above, what is the effective interest rate when the compounding is:

In your responses below, provide two decimal places (with proper rounding) and do NOT include the percent (%) sign.
For example, to provide the response "two and one quarter percent," you would enter 2.25 (and not 2.25% or 0.0225). semiannual? % quarterly? % monthly? %

Answer 1

The effective interest rate when compounding semiannually is approximately 3.82%, when compounding quarterly it is approximately 3.83%, and when compounding monthly it is approximately 3.86%.

Step-by-step explanation:

In order to calculate the effective interest rate when compounding semiannually, quarterly, and monthly, we can use the formula:

Effective Interest Rate (EIR) = (1 + (Nominal Interest Rate / Number of Compounding Periods))Number of Compounding Periods - 1

For a nominal interest rate of 3.80%, the effective interest rates when compounded semiannually, quarterly, and monthly are:

• Semiannual: EIR = (1 + (0.0380 / 2))^2 - 1 ≈ 0.0382 or 3.82%
• Quarterly: EIR = (1 + (0.0380 / 4))^4 - 1 ≈ 0.0383 or 3.83%
• Monthly: EIR = (1 + (0.0380 / 12))^12 - 1 ≈ 0.0386 or 3.86%