In the year 2015 the nominal rate of interest in a country was 6% and the inflation rate was 1.5%. What was the approximate real rate of interest in 2015?

Introduction / Context:
Understanding the difference between nominal and real interest rates is fundamental in macroeconomics and personal finance. The nominal interest rate is the stated rate on a loan or deposit, while the real interest rate adjusts this for inflation to show the true increase in purchasing power. This question tests whether the learner can compute the approximate real rate of interest when given the nominal rate and the inflation rate for a given year.

Given Data / Assumptions:
- Nominal interest rate in 2015: 6%.
- Inflation rate in 2015: 1.5%.
- We are asked to find the real interest rate for that year.
- We use the simple approximation formula for the real interest rate.

Concept / Approach:
The approximate relationship between nominal rate (i), real rate (r) and inflation rate (π) is given by r ≈ i - π, where all rates are expressed as percentages. This approximation is widely used in exam questions because it is simple and accurate enough for moderate inflation rates. For higher precision, one could use the exact Fisher equation r = (1 + i) / (1 + π) - 1, but for small rates the difference between the two formulas is minimal. Here, the approximation is sufficient and easy to apply.

Step-by-Step Solution:
Step 1: Identify the nominal interest rate (i) which is 6%. Step 2: Identify the inflation rate (π) which is 1.5%. Step 3: Use the approximate formula for the real rate: r ≈ i - π. Step 4: Substitute the values: r ≈ 6% - 1.5% = 4.5%. Step 5: Therefore, the approximate real interest rate in 2015 is 4.5%.

Verification / Alternative check:
To check using the exact Fisher equation, convert the percentages to decimal form. Nominal i = 0.06 and inflation π = 0.015. Then r = (1 + 0.06) / (1 + 0.015) - 1 = 1.06 / 1.015 - 1. The ratio 1.06 / 1.015 is approximately 1.0443, so r ≈ 0.0443 or 4.43%. This is very close to 4.5%, confirming that the simple difference method gives a good approximation and that 4.5% is the correct option among those provided.

Why Other Options Are Wrong:
7.50% is wrong because real interest cannot be higher than nominal interest when inflation is positive; subtracting inflation must reduce the rate, not increase it.
4% is wrong because it underestimates the subtraction and would correspond to an inflation rate of 2% instead of the actual 1.5%.
0.25% is wrong because it comes nowhere near the difference between 6% and 1.5%, and would imply an unrealistic inflation situation for the given nominal rate.

Common Pitfalls:
A common mistake is to add the inflation rate instead of subtracting it, which leads to an inflated real rate. Another error occurs when students forget that inflation erodes purchasing power, so the real rate must be smaller than the nominal rate as long as inflation is positive. To avoid confusion, always remember the approximate identity r ≈ nominal rate minus inflation rate, and double check whether the resulting real rate is logically less than the nominal rate when prices are rising.

Final Answer:
The approximate real interest rate in 2015 was 4.50%.