After Tax Real Interest Rate

Real Interest Charge per unit Formula (Tabular array of Contents)

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What is the Real Interest Rate Formula?

The term "real interest rate" refers to the interest charge per unit that has been adjusted by removing the consequence of aggrandizement from the nominal involvement charge per unit. In other words, information technology is finer the actual toll of debt for the borrower or bodily yield for the lender. The formula for real interest rate can be derived by dividing ane plus the nominal interest rate past 1 plus the inflation charge per unit during the menstruum. Mathematically, information technology is represented as,

Real Interest Rate = [(one + Nominal Interest Rate) / (1 + Inflation Rate)] – 1

On the other mitt, the formula for real interest rate tin can be approximated as per Fisher equation and be expressed as the difference between the nominal interest charge per unit and the inflation rate during the period. Mathematically, information technology is represented as,

Real Involvement Rate = Nominal Involvement Charge per unit – Aggrandizement Rate

Examples of Real Interest Rate Formula (With Excel Template)

Let's take an instance to empathize the calculation of Existent Interest Rate in a meliorate manner.

Yous can download this Real Interest Rate Formula Excel Template hither – Real Interest Rate Formula Excel Template

Real Interest Rate Formula – Example #one

Let us accept the example of David who has recently invested a sum of $20,000 in a long term deposit fund. The tenure of the fund is 10 years and the annualized nominal involvement rate offered is 4%. If the inflation rate during the period is expected to be 2%, then calculate the real interest rate equally per the total formula and the approximate formula.

Solution:

Real Interest Charge per unit is calculated using the full formula given below

Existent Interest Rate = [(one + Nominal Interest Rate) / (i + Aggrandizement Rate)] – 1

Real Interest Rate = [(one + 4%) / (ane + ii%)] – 1
Real Involvement Rate = i.96%

Real Involvement Charge per unit is calculated using the gauge formula given beneath

Real Involvement Rate = Nominal Involvement Rate – Inflation Charge per unit

Real Interest Rate = 4% – 2%
Existent Involvement Charge per unit = 2%

Therefore, the real involvement is expected to be 1.96% and 2% according to full and approximate formula respectively.

Real Involvement Rate Formula – Case #2

Allow u.s. take the instance of John who is in the process of making an investment decision. The bank has offered him three interest charge per unit plans –

Quarterly Interest Rate of ane%,
Half-Yearly Involvement Charge per unit of 2% and
Annual Involvement Rate of 4%.

Now, assist John to decide which plan volition offer him the best real involvement rate if the inflation charge per unit during the catamenia is expected to be ii%.

Solution:

Nominal Interest Rate is calculated every bit

For Quarterly

Nominal Involvement Rate = [(one + 1% )⁴ – one]
Nominal Interest Rate = 4.06%

For Half-Yearly

Nominal Interest Rate = [(ane + two% )² – 1]
Nominal Involvement Charge per unit = 4.04%

For Almanac

Nominal Interest Rate = [(1 + 4% )¹ – 1]
Nominal Interest Charge per unit = 4.00%

Existent Interest Charge per unit is calculated using the full formula given below

Existent Involvement Charge per unit = [(1 + Nominal Interest Charge per unit) / (i + Inflation Charge per unit)] – i

For Quarterly

Real Involvement Rate = [(1 + 4.06%) / (1 + 2%)] – ane
Real Interest Charge per unit = ii.02%

For One-half-Yearly

Real Involvement Rate = [(1 + 4.04%) / (1 + ii%)] – 1
Existent Interest Rate = 2.00%

For Annual

Real Interest Charge per unit = [(1 + four.00%) / (1 + 2%)] – 1
Real Interest Rate = 1.96%

From the above results, it can be clearly seen that the one^st pick with a quarterly return of 1% will offer the all-time existent interest rate of return.

Caption

The formula for Real Interest Charge per unit can exist derived by using the following steps:

Pace 1: Firstly, decide the nominal interest charge per unit which is commonly an annual rate of interest documented for any given investment.

Stride 2: Next, decide the inflation rate during the catamenia. Usually, the inflation rate is annualized and it can exist easily available from various authorities databases, such as the U.Due south. Bureau of Labor Statistics. In fact, Treasury Inflation-Protected Securities (TIPS) can be a skillful indicator of inflation charge per unit in the US.

Step three: Finally, The formula for real interest rate tin can be derived by dividing one plus the nominal involvement charge per unit (step 1) by one plus the aggrandizement rate (stride 2) during the flow every bit shown below.

Real Interest Rate = [(1 + Nominal Interest Rate) / (1 + Inflation Charge per unit)] – 1

On the other hand, according to the Fisher equation, the formula for the real interest rate can be derived by deducting the inflation rate during the menses from the nominal involvement charge per unit as shown below.

Real Interest Rate = Nominal Involvement Charge per unit – Inflation Rate

Relevance and Uses of Real Interest Charge per unit Formula

From an investor'southward perspective, it is of import to understand the concept of real involvement rate because information technology captures the real growth of the wealth after adjusting the inflation rate. One needs to be cognizant of the fact that inflation erodes the value of every stream of cash flows, either mainstream like salary or passive like return on investment. As such, information technology is essential that we consider the impact of inflation while making a decision about any investment from which we expect a stream of cash flows in the time to come.