CalculationTime

APY Calculator

Calculate annual percentage yield from a stated interest rate and compounding frequency, with ending balance, earned interest and a printable savings comparison record.

Live math canvas

Your numbers, formula and explanation together

APY Calculator: 4.8548% APY. 10,000.00 at 4.75% compounded 12×/year for 1 year = 10,485.48 ending balance · 485.48 interest · +35.48 versus 4.5% comparison APY

Formula applied

The exact method behind this answer

CalculationTime keeps the method visible so the number can be checked instead of blindly trusted.

APY = (1 + nominal annual rate ÷ compounding periods per year) ^ compounding periods per year − 1. Ending balance = starting balance × (1 + nominal rate ÷ n) ^ (n × years). Interest earned = ending balance − starting balance.
  1. Apply the formulaAPY = (1 + nominal annual rate ÷ compounding periods per year) ^ compounding periods per year − 1. Ending balance = starting balance × (1 + nominal rate ÷ n) ^ (n × years). Interest earned = ending balance − starting balance.4.8548% APY10,000.00 at 4.75% compounded 12×/year for 1 year = 10,485.48 ending balance · 485.48 interest · +35.48 versus 4.5% comparison APY

Your live breakdown

Current inputs in the calculation

These values come from the controls above and update when the calculator changes.

Starting balance
10,000 money
Initial savings, deposit or comparison balance.
Stated annual interest rate
4.75 %
The quoted annual rate before compounding turns it into APY.
Compounding periods per year
12 n
Use 1 annual, 4 quarterly, 12 monthly, 365 daily or the institution’s stated compounding rule.
Time held
1 years
Length of the comparison. APY itself is annual; balance growth uses this time.
Comparison APY
4.5 %
Optional published APY or competing account rate for the printed comparison note.

Resulting answer

4.8548% APY

10,000.00 at 4.75% compounded 12×/year for 1 year = 10,485.48 ending balance · 485.48 interest · +35.48 versus 4.5% comparison APY

Answer
4.8548% APY
Live support
10,000.00 at 4.75% compounded 12×/year for 1 year = 10,485.48 ending balance · 485.48 interest · +35.48 versus 4.5% comparison APY

Assumptions used

What this answer assumes

Best for savings-account comparisons, term-deposit notes, classroom compound-interest examples, personal budget files and quote-ready records where the compounding basis must be visible.

  • The nominal rate is entered as an annual percentage before compounding.
  • Compounding periods are treated as evenly spaced and the rate is assumed constant for the selected time.
  • The calculator does not include deposits, withdrawals, account fees, taxes, promotional-rate expiry, minimum balances or early withdrawal penalties.
  • A comparison APY is shown for planning only; use the official product disclosure or bank terms for decisions.
  • Negative rates are allowed for mathematical completeness, but real accounts may have floor, fee or disclosure rules.

Master’s Tip

How to use the result well

Master’s Tip: compare APY with APY, not stated rate with APY. If one account advertises a nominal rate and another advertises APY, convert them to the same basis before choosing.

Printable record

What belongs in the saved calculation

Save the inputs, result, formula, assumptions, page URL and date together so the calculation can be reviewed later.

Starting balance
10,000 money
Initial savings, deposit or comparison balance.
Stated annual interest rate
4.75 %
The quoted annual rate before compounding turns it into APY.
Compounding periods per year
12 n
Use 1 annual, 4 quarterly, 12 monthly, 365 daily or the institution’s stated compounding rule.
Time held
1 years
Length of the comparison. APY itself is annual; balance growth uses this time.

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Formula

APY = (1 + nominal annual rate ÷ compounding periods per year) ^ compounding periods per year − 1. Ending balance = starting balance × (1 + nominal rate ÷ n) ^ (n × years). Interest earned = ending balance − starting balance.

Worked example

For a 4.75% stated annual rate compounded monthly, APY = (1 + 0.0475 ÷ 12)^12 − 1 = 4.8551%. A 10,000 starting balance held for one year grows to about 10,485.51 before fees, taxes, deposits or withdrawals.

Professional note

Master’s Tip: compare APY with APY, not stated rate with APY. If one account advertises a nominal rate and another advertises APY, convert them to the same basis before choosing.

Regional and unit assumptions

Standard or basis: general compound-interest APY arithmetic. This page is an educational and planning calculator, not financial, banking, tax, investment or product-disclosure advice.

Assumptions and limitations

Methodology & Accuracy

How this calculator is checked

CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.

Formula used

APY = (1 + nominal annual rate ÷ compounding periods per year) ^ compounding periods per year − 1. Ending balance = starting balance × (1 + nominal rate ÷ n) ^ (n × years). Interest earned = ending balance − starting balance.

Standard or basis

Standard or basis: general compound-interest APY arithmetic. This page is an educational and planning calculator, not financial, banking, tax, investment or product-disclosure advice.

Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.

Master's Tip

Master’s Tip: compare APY with APY, not stated rate with APY. If one account advertises a nominal rate and another advertises APY, convert them to the same basis before choosing.

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These cards are resolved from calculator data, category context and live-route status so the page links to useful next steps without hand-built link clutter.

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Questions

What does APY mean?

APY means annual percentage yield. It is the effective one-year return after interest compounding is included.

How do I calculate APY?

Divide the stated annual rate by the number of compounding periods, add 1, raise that to the number of compounding periods, then subtract 1.

Is APY higher than the stated interest rate?

Usually yes when the rate is positive and compounds more than once per year. More frequent compounding makes APY slightly higher than the nominal stated rate.

Does this APY calculator include taxes or fees?

No. It shows gross compound-interest arithmetic before taxes, account fees, minimum-balance rules, deposits, withdrawals or promotional-rate changes.

What should I print for an APY comparison?

Print the starting balance, stated rate, compounding frequency, APY, ending balance, interest earned, comparison APY, formula, date, page URL and notes area.

Calculation note

APY exists because a stated annual rate does not tell the whole story when interest compounds during the year. A clear comparison names the compounding frequency, shows the effective annual yield and keeps fees or taxes outside the pure formula.

Compounding changes the annual result

When interest is credited more than once per year, each later period can earn interest on earlier interest. APY expresses that compounded result as one annual percentage.

APY helps compare different account structures

Two accounts can quote similar rates but compound at different frequencies. Converting both to APY makes the comparison more consistent before fees, limits and account rules are considered.

The printed record should keep disclosures separate

The mathematical yield is only one part of a real banking decision. Fees, tax treatment, promotional windows, balance requirements and withdrawal rules belong in the notes or official product disclosure.

Sources and further readingConsumer Financial Protection Bureau — What is APY?FDIC — Truth in Savings ActFederal Reserve — Regulation DD, Truth in Savings