In 2015, the nominal rate of interest in a country was 5.5 percent and the inflation rate was 2.5 percent. What was the approximate real rate of interest in 2015?

Introduction / Context:
When people talk about interest rates, they often refer to the nominal rate, which is the rate quoted by banks and financial institutions. However, what really matters for purchasing power is the real rate of interest, which adjusts the nominal rate for inflation. This question tests understanding of the basic relationship between nominal, real, and inflation rates, using simple data for a particular year.

Given Data / Assumptions:

• The nominal interest rate in 2015 was 5.5 percent.
• The inflation rate in the same year was 2.5 percent.
• The question asks for the real interest rate, which measures the increase in purchasing power.
• We assume inflation is relatively low and use the simple approximation that real rate is nominal rate minus inflation.

Concept / Approach:
The real interest rate adjusts the nominal interest rate for the erosion of purchasing power caused by inflation. A commonly used approximation, valid when rates are low, is that real rate equals nominal rate minus inflation rate. In more exact form, real rate is approximately equal to (1 + nominal rate) divided by (1 + inflation rate) minus 1, but for moderate rates the difference between the approximate and exact value is small. In this question, subtracting the inflation rate of 2.5 percent from the nominal rate of 5.5 percent yields a real rate of roughly 3 percent.

Step-by-Step Solution:
Step 1: Write down the nominal interest rate, which is 5.5 percent.Step 2: Write down the inflation rate, which is 2.5 percent.Step 3: Use the approximate formula for the real interest rate: real rate = nominal rate minus inflation rate.Step 4: Perform the subtraction: 5.5 minus 2.5 equals 3.0.Step 5: Interpret the result as a real interest rate of about 3 percent.Step 6: Compare with the options and select 3 percent as the correct answer.

Verification / Alternative check:
To verify using the exact formula, convert percentages to decimals. Nominal rate is 0.055 and inflation rate is 0.025. Compute the exact real rate as (1 + 0.055) divided by (1 + 0.025) minus 1. This equals 1.055 divided by 1.025 minus 1, which is approximately 1.0293 minus 1, or about 0.0293, that is 2.93 percent. Rounded to the nearest whole number, this is 3 percent, confirming that the approximate method of subtracting inflation from the nominal rate gives a very similar answer for moderate rates.

Why Other Options Are Wrong:
An 8 percent real interest rate would be higher than the nominal rate and is impossible given positive inflation, so option a is incorrect. The value 2.2 percent is not obtained by either the approximate or exact calculation, so option b is incorrect. The very high value 13.75 percent is unrelated to the given data and is clearly wrong. The nominal rate of 5.5 percent is what you obtain before adjusting for inflation; it is not the real rate, so option e is incorrect.

Common Pitfalls:
Some learners forget to subtract inflation and simply report the nominal rate, which overstates the gain in purchasing power. Others may subtract in the wrong direction or make arithmetic mistakes. A simple way to remember the relationship is that real rate is nominal rate minus inflation rate when rates are moderate. Practising a few examples helps reinforce this concept and reduce errors in examination.

Final Answer:
The approximate real rate of interest in 2015 was 3 percent.