Nominal Interest Rate VS Real Interest Rate

What is a Nominal Interest Rate?

The nominal interest rate is the interest rate applied when lending or borrowing money. Simply put, it's the interest rate you receive when you save money in a bank or the interest rate you pay when you take out a loan.

Understanding Through Examples

Example 1: Savings

• You save $1,000 in a bank for one year at a nominal interest rate of 5% per annum.
• The interest earned after one year is $1,000 * 5% = $50.
• Therefore, the total amount received at maturity is $1,000 + $50 = $1,050.

Example 2: Loan

• You borrow $1,000 from a bank for one year at a nominal interest rate of 10% per annum.
• The interest to be paid after one year is $1,000 * 10% = $100.
• Therefore, the total amount to be repaid at maturity is $1,000 + $100 = $1,100.

Organizing in a Table

DivisionAmount (USD)Nominal Interest Rate (%)Period (Years)Interest (USD)Maturity Amount (USD)

Savings	1,000	5	1	50	1,050
Loan	1,000	10	1	100	1,100

Nominal Interest Rate vs. Real Interest Rate

The nominal interest rate is simply the interest rate expressed in terms of the amount of money. However, the interest rate we actually feel is the real interest rate, which takes the inflation rate into account. For example, if the nominal interest rate is 5% and the inflation rate is 3%, the real interest rate is 2%. This means that because the value of money has decreased by 3%, the actual profit earned is only 2%.

Key Takeaways:

• The nominal interest rate is the interest rate applied when lending or borrowing money.
• The nominal interest rate is the standard for earning interest when saving and paying interest when borrowing.
• You can find out the interest rate you actually feel (real interest rate) by considering both the nominal interest rate and the inflation rate.

Real Interest Rates Explained

The real interest rate is the interest rate that is actually felt after taking the inflation rate into account. In other words, even if the nominal interest rate is high, if prices rise significantly, the actual profits received will decrease.

Example:

• You save $1,000 in a bank for one year at a nominal interest rate of 5% per annum.
• One year later, you receive $1,050, but prices have risen by 3% in the meantime.
• The actual purchasing power of $1,050 is almost similar to the purchasing power of $1,000 a year ago ($1,050 / 1.03 ≒ $1,019.42).
• So the real interest rate is about 2% (5% - 3% = 2%).

Another Example:

• If the nominal interest rate is 10% and the inflation rate is 8%, the real interest rate is 2%.
• If the nominal interest rate is 3% and the inflation rate is 5%, the real interest rate is -2%. (In other words, you are losing money.)

By understanding nominal and real interest rates, you can better grasp how inflation affects your savings and loans.

 

What is a Real Interest Rate?

The real interest rate is the interest rate that has been adjusted for inflation. It represents the actual purchasing power of the interest earned or paid. In other words, it shows how much you actually gain or lose after accounting for changes in the price level.

Formula

Real Interest Rate=Nominal Interest Rate−Inflation Rate

Understanding Through Examples

Example 1: Savings

1. Scenario: You save $1,000 in a bank for one year at a nominal interest rate of 5% per annum.
2. Calculation:
   • Nominal Interest Earned: $1,000 \times 5% = $50
   • Total Amount After One Year: $1,000 + $50 = $1,050
3. Inflation Rate: Suppose the inflation rate over the year is 3%.
4. Real Interest Rate Calculation: Real Interest Rate=5%−3%=2%
5. Purchasing Power: After one year, $1,050 in terms of purchasing power is:

                 So, the purchasing power of your savings increased by approximately $19.42.

Example 2: Loan

1. Scenario: You borrow $1,000 from a bank for one year at a nominal interest rate of 10% per annum.
2. Calculation:
   • Nominal Interest to be Paid: $1,000 \times 10% = $100
   • Total Repayment Amount After One Year: $1,000 + $100 = $1,100
3. Inflation Rate: Suppose the inflation rate over the year is 8%.
4. Real Interest Rate Calculation: Real Interest Rate=10%−8%=2%
5. Purchasing Power: The actual cost in terms of purchasing power to repay the loan after one year is: 

             So, the actual cost of the loan in terms of purchasing power increased by approximately $18.52.

Organizing in a Table

DivisionAmount (USD)Nominal Interest Rate (%)Inflation Rate (%)Real Interest Rate (%)Total Amount After 1 Year (USD)Purchasing Power Adjusted (USD)

Savings	1,000	5	3	2	1,050	1,019.42
Loan	1,000	10	8	2	1,100	1,018.52

 

Conclusion

The real interest rate gives you a clearer picture of the true cost of borrowing or the true gain from saving money after accounting for inflation. It's an essential concept to understand when evaluating the profitability of investments or the cost of loans.