Effective Annual Rate – 4% nominal compounded quarterly: Find the effective annual rate corresponding to a nominal 4% per annum compound interest paid quarterly.

Introduction / Context:
The effective annual rate (EAR) converts a nominal rate with intra-year compounding into a single equivalent annual rate that yields the same one-year growth. This is vital for comparing products with different compounding frequencies on an apples-to-apples basis.

Given Data / Assumptions:

• Nominal annual rate r_nom = 4%
• Compounding frequency m = 4 (quarterly)
• We seek: EAR = (1 + r_nom/m)^m − 1

Concept / Approach:
Plug in r_nom = 0.04 and m = 4. The per-quarter rate is 0.04/4 = 0.01; raising 1.01 to the 4th power gives the one-year growth multiplier, from which we subtract 1 to obtain the effective rate.

Step-by-Step Solution:
Per-quarter factor = 1 + 0.04/4 = 1.01Annual growth factor = (1.01)^4 = 1.04060401EAR = 1.04060401 − 1 = 0.04060401 ≈ 4.0604%

Verification / Alternative check:
Compare simple annual interest of 4% (EAR 4.00%) to quarterly compounding (EAR ≈ 4.0604%); the latter is slightly higher due to interest-on-interest within the year.

Why Other Options Are Wrong:
4.604%, 5.0605%, and 5.605% are too large for only quarterly compounding at 4%; 4.0000% ignores intra-year compounding entirely.

Common Pitfalls:
Multiplying 4% by 4 or dividing without exponentiation is incorrect. Always use the compounding formula to translate nominal to effective rates.

Final Answer:
4.0604%