Final answer:
The effective annual interest rate (EAR) with continuous compounding at a nominal rate of 4.6% is approximately 4.72%. To calculate EAR the formula e^r - 1 is used, where r is the nominal interest rate. There would be a notable difference in EAR when comparing it with interest rates of 4% and 5%.
Step-by-step explanation:
The question asks to determine the effective annual interest rate (EAR) when the nominal interest rate is 4.6% with continuous compounding. To compute the EAR in case of continuous compounding, the formula used is E = er - 1, where E is the effective annual rate and r is the nominal rate expressed as a decimal. In this case, for a nominal rate of 4.6%, or 0.046, the EAR would be calculated as E = e0.046 - 1.
Calculating it further, we have E = e0.046 - 1 ≈ 0.0472, or 4.72%. So, the effective annual interest rate with continuous compounding at a nominal rate of 4.6% is approximately 4.72%.
When comparing the accumulation for interest rates of 4% and 5% with the same continuous compounding, you would expect to see a difference in the effective annual interest rates as well. A lower nominal rate of 4% would yield a lower EAR, and a higher nominal rate of 5% would result in a higher EAR, demonstrating the sensitivity of accumulation to changes in interest rates.