The periodic interest rate on an investment is 1.75% per quarter. What is the equivalent nominal annual rate of interest, quoted per annum, that corresponds to this quarterly rate?

Introduction / Context:
This question checks your understanding of nominal and periodic interest rates. Financial institutions often quote an annual nominal rate but actually apply interest at shorter intervals such as monthly, quarterly, or half yearly. In some problems, the periodic rate is given and you must work out the corresponding nominal annual rate. Being able to move between these two views of the same rate is an important skill in time value of money calculations and in interpreting bank advertisements and loan offers correctly.

Given Data / Assumptions:

• Periodic rate per quarter i = 1.75% per quarter
• There are 4 quarters in one year
• We are asked for the nominal annual rate of interest
• The nominal rate is quoted without converting it to an effective annual rate

Concept / Approach:
The nominal annual rate is simply the periodic rate multiplied by the number of compounding periods per year. It is a way of quoting the rate in per year terms but does not reflect compounding within the year. In this question, the compounding period is a quarter, so there are 4 compounding periods in one year. Therefore, the nominal annual rate j is given by j = periodic rate * number of periods per year. We do not yet convert this to an effective annual yield, we only scale the periodic rate linearly by the number of periods.

Step-by-Step Solution:
Given periodic rate per quarter i = 1.75% Number of quarters per year m = 4 Nominal annual rate j = i * m j = 1.75% * 4 j = 7.00% per annum

Verification / Alternative check:
You can think of this as simply adding 1.75% four times over the year since nominal rates do not yet incorporate the effect of compounding. If we wanted the effective annual rate, we would calculate (1 + 0.0175)^4 - 1, which gives a slightly higher percentage. However, the question clearly asks for the nominal rate, so the simple multiplication approach is exactly what is needed and the result of 7% per annum is correct.

Why Other Options Are Wrong:
8% and 9% per annum would correspond to periodic rates of 2% or 2.25% per quarter, which do not match the given 1.75%. A 10% nominal rate would imply 2.5% per quarter, which is also inconsistent. Therefore 7% per annum is the only option that correctly reflects four quarters at 1.75% each.

Common Pitfalls:
Learners sometimes confuse the nominal annual rate with the effective annual rate, which includes compounding. Another error is to divide by 4 instead of multiplying, which would be appropriate only if you were given a nominal annual rate and asked for the periodic rate. Reading the phrase per quarter carefully helps avoid this confusion.

Final Answer:
The nominal annual rate of interest is 7% per annum corresponding to a periodic rate of 1.75 percent per quarter.