Final answer:
To find the nominal annual rate of interest compounded quarterly equivalent to 4.1% compounded monthly, we calculate the effective annual rate (EAR) for 4.1% monthly and then find the corresponding nominal rate for quarterly compounding, which comes out to approximately 4.1%. The closest listed answer is (c) 4.2%.
Step-by-step explanation:
The subject of the question is to find the nominal annual rate of interest compounded quarterly that is equivalent to an interest rate of 4.1% compounded monthly. To solve this, we must use the concept of the effective annual rate (EAR) as an intermediate step.
Firstly, to find the EAR of a 4.1% interest rate compounded monthly, we use the formula EAR = (1 + i/n)^n - 1, where i is the nominal annual interest rate and n is the number of compounding periods per year. For a monthly rate, n = 12.
EAR = (1 + 0.041/12)^12 - 1 = (1 + 0.00341667)^12 - 1 ≈ 0.0416184 or 4.16184%
Next, we find the nominal annual rate compounded quarterly that would give us the same EAR. For quarterly compounding, n = 4. We can rearrange the EAR formula to solve for i:
i = [(1 + EAR)^(1/n) - 1] * n
i = [(1 + 0.0416184)^(1/4) - 1] * 4 ≈ 0.040948 or 4.0948%
Thus, the nominal annual rate compounded quarterly equivalent to 4.1% compounded monthly is approximately 4.1%, which is closest to option (c) 4.2%.