Compound interest calculator

It evaluates the discrete identity in pure arithmetic so a worksheet, a coaching session, and an API client never disagree.

Input contract, response shape, and error behaviour

Example: one thousand principal, five percent, twelve compounds per year, and ten years yields one hundred twenty periods, a final balance of one thousand six hundred forty-seven point zero one, and interest of six hundred forty-seven point zero one. The same principal and rate compounded only once per year for ten years yields a smaller balance of one thousand six hundred twenty-eight point eight nine, which is the point of exposing frequency as its own field. Failed validation does not consume balance. POST a JSON body with four required finite numbers. principal is the starting amount in one currency; aliases amount, p, and starting_balance are accepted so spreadsheets can keep familiar column names, and the value must sit between zero and one trillion inclusive. rate is the nominal annual percent—five means five percent per year—not a decimal 0.05 unless you truly intend five hundredths of a percent; aliases annual_rate, annual_percent, and interest_rate map to the same field. If rate is missing, empty, infinite, or otherwise not a finite number, the task fails with invalid_input naming rate; that is the contracted error and it is not billed. frequency is n, an integer from one through three hundred sixty-five compounding periods per year, with aliases n, compounds_per_year, and compounding_frequency. years is t, a finite number from zero through one hundred twenty; fractional years such as two point five are allowed, and aliases t, time, and periods_years are accepted. Each field may arrive as a JSON number or a numeric string. On success the body echoes principal, rate, frequency, and years, reports periods as n times t, and returns final_balance and interest rounded half-up to two decimal places for stable currency-style goldens, plus a formula string restating A equals P times one plus r over n to the n t.

Where a compound interest API earns its keep

Households and students use a compound interest calculator when a savings balance, a certificate of deposit, or a homework problem asks how much a lump sum grows at a stated annual rate with a stated posting frequency. Personal-finance coaches need a deterministic oracle that rejects a non-finite rate instead of silently showing NaN that a buggy form might treat as success. When you later need regular deposits, switch to a future-value-of-annuity identity rather than stretching this four-field lump-sum contract. Product teams wire the same contract into onboarding demos so a user who types a principal, a percent, monthly compounding, and a horizon sees the identical final_balance the API will later return in production tests. Keep requests small, pin rounded final_balance and interest in tests, and you get reproducible future values for worksheets, LMS plugins, and edge workers without standing up a spreadsheet service of your own.