APR vs APY vs Investment Return

Borrowing: distinguish the note rate from APR

The mortgage note interest rate is used to calculate interest on the outstanding loan. Mortgage APR expresses a broader annualized cost that includes specified fees and charges. CFPB explains that APR can therefore differ from the stated interest rate even for the same loan.

MoneyBasis’s mortgage calculator needs the note rate to amortize principal and interest. It does not calculate a regulatory APR from an origination-fee schedule. Entering an APR that includes fees into the note-rate field can overstate the periodic interest being charged on the balance.

The Loan Payoff and Debt Snowball tools use an APR-style monthly planning convention: the entered annual percentage divided by twelve. This is a simplified borrowing-rate input, not a full reconstruction of all credit disclosures, daily balances or fees. Real contracts may accrue interest daily, have promotional periods or use other rules.CFPB

APY already includes compounding

Annual percentage yield expresses a deposit account’s annual interest yield with compounding reflected in it. Regulation DD defines it using the interest rate, compounding frequency and specified annual calculation rules. For a fixed rate with interest retained, it answers a different question from simply multiplying a periodic rate by the number of periods.

For a nominal annual rate a compounded k times per year, the effective annual yield is (1 + a/k)^k − 1. A 12% nominal annual rate compounded monthly has a 1% monthly rate and an effective annual yield of 12.6825%.

A quoted 5% APY therefore is not generally the same as a 5% nominal rate compounded monthly. The latter includes additional compounding on top of the nominal rate. Actual account disclosures also matter when rates vary, balances have tiers or fees apply.CFPB

Worked example

Worked examples: translate rates without changing the question

In a loan example with $10,000 outstanding and a 12% annual input divided by twelve, first-month interest is $100. If a $300 payment follows, $200 reduces principal and the closing balance is $9,800. The interest calculation concerns a debt balance and payment, not an investment yield.

For a deposit comparison, $10,000 earning a fixed 5% APY for a full year with no withdrawals would reach $10,500 before any separate fees or taxes. In MoneyBasis’s compound calculator, 5% with annual compounding reproduces that full-year growth. To use monthly compounding with the same effective annual yield, the nominal annual input is 12 × (1.05^(1/12) − 1), expressed as a percentage: approximately 4.888949%.

The table places equivalent and nonequivalent rates side by side. These conversions say nothing about the likelihood that a market investment will earn a specified return.

An investment input is a scenario assumption

MoneyBasis’s compound-interest field takes a nominal annual investment rate paired with a frequency. Its monthly-equivalent growth factor is derived from those two inputs. A historical annualized total return quoted elsewhere may instead be an effective geometric return over a particular period. Copying it into a nominal monthly-compounding field changes the effective annual assumption.

Market total return can include changes in price and distributions. It is not the same as a deposit contract’s yield, and it need not remain positive. Reinvestment, fees and taxes affect the amount available to grow. The calculator does not separately deduct those costs or recreate the volatility of the underlying asset.

A rate can also be before or after inflation. Compounding frequency and purchasing-power adjustment answer separate questions. An effective annual return can still be nominal in the sense of not inflation-adjusted; “nominal” has both a rate-convention meaning and a dollar-basis meaning, so the surrounding description matters.SEC

Before copying a rate

A short check before copying a rate

Identify the object first: a debt balance, a deposit account or a market investment. Next identify whether the percentage includes fees or compounding. Finally identify its period and whether it is before or after inflation, taxes and investment costs.

Use a note rate for mortgage interest. Use the documented annual-rate-divided-by-twelve convention for simplified payoff schedules, with its contract limitations understood. For Compound Interest, pair the input with the intended frequency or convert an effective yield to its nominal equivalent.

The rate conversion table assumes fixed rates, retained interest and no withdrawals or fees. It is not an offer, a product comparison or a recommended return. An accurate conversion preserves a specified growth assumption; it cannot make uncertain growth certain.