Compound growth, costs and real return

Simple interest and compounding answer different questions

Simple interest applies the stated rate to the initial principal for the stated time. Compound growth applies each period's rate to the balance then in the account. For a fixed nominal annual rate r compounded n times a year over t years, the teaching formula is FV = P(1 + r/n)^(nt). The actual contract controls how a real product accrues and posts interest.

Nominal return describes a money amount before inflation adjustment; a real-return calculation accounts for inflation and, depending on the definition, taxes. Investor.gov's glossary includes taxes and inflation in its definition. This lesson's worked real calculation excludes tax and says so explicitly.

Evidence: Inputs and compounding frequency · Definition of real return

The page identifies principal, annual rate, time, contributions and compounding frequency as separate inputs. This lesson independently computes hypothetical values and does not project any product.

The glossary defines real return after accounting for taxes and inflation. The worked exercise shows a separate pre-tax purchasing-power adjustment and explicitly excludes taxes.

Reproduce one fictional monthly-compounding result

Every value is invented. Start with P = 1,000 MU, a fixed nominal annual rate r = 6%, monthly compounding n = 12, and t = 1 year; assume no contributions or withdrawals. FV = 1,000 × (1 + 0.06/12)^12 = 1,061.68 MU when rounded to cents. The effective annual growth before costs is about 6.1678%, because the monthly interest also compounds.

Evidence: Inputs and compounding frequency

The page identifies principal, annual rate, time, contributions and compounding frequency as separate inputs. This lesson independently computes hypothetical values and does not project any product.

Subtract the fictional fee, then adjust for purchasing power

Now assume a single fictional 12 MU fee at the end: 1,061.68 − 12 = 1,049.68 MU nominal net balance. Suppose the same fictional basket costs 3% more over that year. Approximate real balance in starting-period MU = 1,049.68 ÷ 1.03 = 1,019.11 MU. The real change after this one fee is (1,019.11 ÷ 1,000 − 1) × 100 ≈ +1.91%, before tax.

Evidence: Definition of real return · BLS CPI basket and limitations

The glossary defines real return after accounting for taxes and inflation. The worked exercise shows a separate pre-tax purchasing-power adjustment and explicitly excludes taxes.

The BLS FAQ describes U.S. CPI populations, representative baskets, weighting and limits: CPI does not describe every individual’s prices or a complete cost of living. This U.S. reference is not a universal measure. The teaching basket here is synthetic.

A calculator output is not a crypto forecast

The example assumes a fixed rate and fixed contribution pattern; a cryptoasset has no guaranteed growth rate from this calculation. A BNB price change, gas payment, exchange fee, pool loss, product lockup, default, tax or changing rate could alter an actual outcome. A Binance exchange offer and a BNB Chain protocol are separate arrangements with separate terms; neither is represented by this fictional compound-interest calculation.

Evidence: Inputs and compounding frequency · Definition of real return · BLS CPI basket and limitations

The page identifies principal, annual rate, time, contributions and compounding frequency as separate inputs. This lesson independently computes hypothetical values and does not project any product.

The glossary defines real return after accounting for taxes and inflation. The worked exercise shows a separate pre-tax purchasing-power adjustment and explicitly excludes taxes.

The BLS FAQ describes U.S. CPI populations, representative baskets, weighting and limits: CPI does not describe every individual’s prices or a complete cost of living. This U.S. reference is not a universal measure. The teaching basket here is synthetic.

Exercise and worked solution

Change only the fictional end fee from 12 MU to 30 MU. Keep every other assumption, including 3% basket inflation. Recalculate the nominal net balance and its purchasing-power value in starting-period MU.

Evidence: Inputs and compounding frequency · Definition of real return · BLS CPI basket and limitations

The page identifies principal, annual rate, time, contributions and compounding frequency as separate inputs. This lesson independently computes hypothetical values and does not project any product.

The glossary defines real return after accounting for taxes and inflation. The worked exercise shows a separate pre-tax purchasing-power adjustment and explicitly excludes taxes.

The BLS FAQ describes U.S. CPI populations, representative baskets, weighting and limits: CPI does not describe every individual’s prices or a complete cost of living. This U.S. reference is not a universal measure. The teaching basket here is synthetic.