Interest Calculator (Simple vs Compound)

Use this interest calculator to find your ending balance and total interest for savings/investing (compound) or a simple-interest loan, over a time length you choose.

How to use our Interest Calculator (Simple vs Compound)

1. Choose what you are calculating: Savings/Investment (money grows) or Simple-interest loan (interest cost).
2. Enter the starting amount (USD): your starting balance for savings, or the amount borrowed for a loan.
3. Enter the annual interest rate (percent). Example: type 5 for 5% per year.
4. Enter the time length, then pick years or months (months are converted using 12 months = 1 year).
5. Open Advanced options if you want compounding, contributions, APY/APR conversion, rate comparison, or different rounding.
6. In savings mode, pick a compounding frequency (monthly is common). If you pick continuous, contributions are approximated using frequent steps.
7. If you add money over time, enter the contribution each period and choose how often you contribute and whether you add it at the start or end of each period.
8. If needed, set Rate type you entered to APR or APY, then keep the compounding frequency set so the calculator can convert correctly.
9. Optional: enter a rate variance (percent) to see low, base, and high ending balances.
10. Click Calculate to see the ending balance, total interest, effective APY, and the balance schedule table.

Definitions

Principal (starting amount): The money you start with (savings) or the amount you borrow (loan).

Interest: Extra money earned (savings) or paid (loan) because money is used over time [2].

Annual interest rate (percent): The stated yearly rate. Example: 5 means 5% per year [3].

Simple interest: Interest calculated only on the original principal (it does not earn interest on past interest).

Compound interest: Interest that gets added to the balance, so future interest is calculated on a bigger amount (interest on interest) [1].

Compounding frequency: How often interest is added to the balance (yearly, monthly, daily, or continuous).

Contribution: Extra money you add each period in savings mode (can be negative if you withdraw).

APR: Annual Percentage Rate, a stated annual rate (often used for borrowing).

APY: Annual Percentage Yield, the yearly growth rate after considering compounding (often used for saving).

Methodology

Inputs and units

Time is converted to years as: time in years = time length if you choose years, or time length divided by 12 if you choose months. The annual interest rate (percent) is converted to a decimal rate by dividing by 100.

Mode: Simple-interest loan

This mode uses simple interest on the original principal only: ending balance A = principal P * (1 + annual rate r * time in years t). Total interest = A - P. (This is an estimate of interest cost when interest does not compound and nothing is paid until the end.)

Mode: Savings/Investment (compound)

If there are no contributions and compounding is not continuous, the calculator uses A = P * (1 + r/n)^(n*t), where n is the number of compounds per year (yearly 1, quarterly 4, monthly 12, daily 365). If continuous is selected and there are no contributions, it uses A = P * e^(r*t). These match the standard idea of compound interest [1].

Contributions, mismatched frequencies, and timing (simulation)

When contributions are used (or when continuous compounding is selected with contributions), the calculator simulates the balance step-by-step to avoid confusion when contribution frequency and compounding frequency do not match. It chooses a step size based on the smaller period among the selected compounding frequency and contribution frequency (monthly is used for continuous). Each step applies interest for that step, then applies the contribution if it is scheduled for that step. For end timing: balance = balance * (1 + rate per step) + contribution. For start timing: balance = (balance + contribution) * (1 + rate per step). If contributions are set to none, contribution amount is treated as 0 and the timing input is hidden.

APR and APY handling

If Rate type you entered is APR, the calculator treats your rate as the stated annual rate r. If Rate type you entered is APY, it converts APY to an equivalent APR for the selected compounding frequency n using: APR = n * ((1 + APY)^(1/n) - 1). Then it uses that APR in the chosen interest math. The output Effective APY is computed from APR and compounding using: APY = (1 + r/n)^n - 1. (For continuous compounding, effective APY is computed as e^r - 1.)

Rate variance comparison (optional)

If you enter a rate variance v (percent), the calculator also runs the same calculation at three annual rates: (rate - v), (rate), and (rate + v). It shows the three ending balances so you can see how sensitive the result is to the rate.

Outputs

Ending balance is the final total amount. Total contributions added is the sum of all deposits (or withdrawals if negative) in savings mode. Total interest (earned or paid) is ending balance minus starting amount minus total contributions in savings mode, and ending balance minus principal in loan mode. Average interest per year is total interest divided by time in years. The balance schedule shows each step with starting balance, contribution, interest added, and ending balance for that step.

Validation and edge cases

The annual interest rate (percent) is required and cannot be blank. Time length must be greater than 0. If rate variance makes (rate - variance) less than -100%, the calculator shows an error because a rate below -100% is not meaningful. Very large inputs that would overflow are shown as N/A with a short note instead of Infinity. Negative contributions are allowed in savings mode; if the balance goes negative during the schedule, the calculator keeps calculating and adds a note so you do not misread the result.

Sources