Determine the nominal annual rate of interest, convertible quarterly, if the periodic interest rate is 1.75% per quarter.

Introduction / Context:
This question is about converting a periodic interest rate into its corresponding nominal annual rate. In financial mathematics, nominal annual rate is the stated yearly rate that is associated with a given compounding frequency, such as quarterly, monthly or semiannually.

Given Data / Assumptions:

Periodic rate per quarter = 1.75%.

Compounding frequency = quarterly (4 times per year).

We need the nominal annual rate of interest, convertible quarterly.

Concept / Approach:
For a nominal annual rate R (convertible m times per year), the periodic rate i is: i = R / m. Conversely, if we know i and m, we can recover R: R = i * m. Here, i is given as 1.75% per quarter and m = 4.

Step-by-Step Solution:
Step 1: Identify i and m. i = 1.75% per quarter. m = 4 quarters per year. Step 2: Compute the nominal annual rate. R = i * m = 1.75% * 4. R = 7% per annum (nominal, convertible quarterly).

Verification / Alternative check:
We can check whether this makes sense. A nominal 7% annual rate compounded quarterly corresponds to a periodic rate of 7% / 4 = 1.75%, which matches the given periodic rate. Therefore, the conversion is consistent.

Why Other Options Are Wrong:
An 8% nominal rate would imply a quarterly rate of 2%, not 1.75%. Similarly, 9% or 10% nominal would correspond to even higher periodic rates. Only 7% nominal produces the given quarterly rate of 1.75%.

Common Pitfalls:
A common misunderstanding is to confuse nominal and effective annual rates. Some may incorrectly compound 1.75% four times and call that the nominal rate. In fact, that would give the effective annual rate. Here, the question specifically asks for the nominal annual rate, which is simply periodic rate multiplied by the number of periods per year.

Final Answer:
The nominal annual rate of interest (convertible quarterly) is 7%.