Find the effective annual rate of interest for an investment that earns a nominal rate of 5.5% per year when the interest is compounded continuously.

Introduction:
This question deals with continuous compounding, a concept from higher finance and mathematics. Instead of compounding interest yearly, quarterly, or monthly, continuous compounding assumes that interest is added at every instant. We are asked to convert a nominal continuous compounding rate of 5.5% per year into an equivalent effective annual rate.

Given Data / Assumptions:

• Nominal annual rate for continuous compounding r = 5.5% per year.
• We are using the continuous compounding model.
• We seek the effective annual rate r_eff that produces the same growth over one year.

Concept / Approach:
For continuous compounding, the amount A after t years from principal P is:
A = P * e^(r * t)where r is expressed as a decimal and e is the base of natural logarithms. Over one year (t = 1), the effective annual rate r_eff is defined so that:
A = P * (1 + r_eff)Setting these equal gives:
P * (1 + r_eff) = P * e^rTherefore:
1 + r_eff = e^rand so:
r_eff = e^r - 1

Step-by-Step Solution:
Step 1: Convert the nominal rate to decimal: r = 5.5% = 0.055.Step 2: Use the formula for effective rate under continuous compounding: r_eff = e^r - 1.Step 3: Compute e^0.055. This is approximately 1.05654.Step 4: Subtract 1 to find the effective rate: r_eff = 1.05654 - 1 = 0.05654.Step 5: Convert back to percentage: r_eff ≈ 5.654% ≈ 5.65%.Thus, the effective annual rate is approximately 5.65%.

Verification / Alternative check:
We can compare growth factors: under continuous compounding at 5.5%, one rupee becomes approximately 1.05654 rupees in one year. Under an effective annual rate of 5.65%, one rupee becomes 1.0565 rupees. These are virtually identical, confirming that 5.65% is an accurate rounded effective rate.

Why Other Options Are Wrong:
5.75%, 5.85%, and 5.95% all correspond to growth factors of 1.0575, 1.0585, and 1.0595 respectively, each larger than e^0.055. The 5.50% option simply repeats the nominal rate and ignores the impact of continuous compounding, which always yields a slightly higher effective rate for positive interest rates.

Common Pitfalls:
Many students mistakenly treat the nominal rate as the effective rate, or try to use discrete compounding formulas such as (1 + r/n)^n. Continuous compounding uses the exponential function e^(r * t), which must be handled correctly. Always remember to convert the percentage to decimal, use r_eff = e^r - 1 for one year, and then convert back to percent form.

Final Answer:
The effective annual rate of interest corresponding to a nominal 5.5% per year compounded continuously is approximately 5.65%.