Real Return Calculator Formula

Understand the math behind the real return calculator. Each variable explained with a worked example.

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Formulas Used

Real Return Rate

real_return = ((1 + nominal_return / 100) / (1 + inflation_rate / 100) - 1) * 100

Nominal Future Value

nominal_value = initial_amount * pow(1 + nominal_return / 100, years)

Real Future Value (Today's $)

real_value = initial_amount * pow((1 + nominal_return / 100) / (1 + inflation_rate / 100), years)

Purchasing Power Loss

purchasing_power_loss = initial_amount * pow(1 + nominal_return / 100, years) - initial_amount * pow((1 + nominal_return / 100) / (1 + inflation_rate / 100), years)

Variables

VariableDescriptionDefault
nominal_returnNominal Return(%)10
inflation_rateInflation Rate(%)3
initial_amountInvestment Amount(USD)10000
yearsTime Period(years)10

How It Works

Real vs Nominal Returns

The Fisher Equation

Real Return = [(1 + Nominal) / (1 + Inflation)] - 1

This is more accurate than simply subtracting inflation from the nominal return.

Why Real Returns Matter

Nominal returns tell you how much your money grows. Real returns tell you how much your purchasing power grows. If investments grow 10% but prices rise 3%, your actual wealth gain is about 6.8%.

Historical Real Returns

| Asset | Nominal | Real | |---|---|---| | US Stocks | ~10% | ~7% | | US Bonds | ~5% | ~2% | | Cash/Savings | ~3% | ~0% |

Worked Example

10% nominal return, 3% inflation, $10,000 over 10 years.

nominal_return = 10inflation_rate = 3initial_amount = 10000years = 10
  1. 01Real return = (1.10 / 1.03) - 1 = 6.80%
  2. 02Nominal value = $10,000 x (1.10)^10 = $25,937
  3. 03Real value = $10,000 x (1.068)^10 = $19,307
  4. 04Purchasing power loss = $25,937 - $19,307 = $6,630

Ready to run the numbers?

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