Finance Calculator

What this finance calculator does

This calculator solves the basic time-value-of-money relationship between present value, periodic payment, future value, interest rate, and the number of periods. Choose the tab for the missing variable and enter the other four. It is the same relationship used in many loan, savings, and annuity calculations.

The calculator accepts signed cash flows. A positive value is money received, and a negative value is money paid. For example, a deposit may be entered as a positive present value while a withdrawal is entered as a negative payment.

How to use this calculator

1. Choose FV, PMT, I/Y, N, or PV for the value you want to solve.
2. Enter the known amounts with the correct cash-flow signs.
3. Enter the annual interest rate and the number of periods.
4. Open the settings to set payments per year, compounding per year, and whether payments occur at the beginning or end of each period.
5. Click Calculate.

The default example starts with a present value of $20,000, a payment of -$2,000 per period, 10 periods, and a 6% annual rate. Solving for future value gives -$9,455.36.

Time-value-of-money formula

For end-of-period payments:

FV + PV × (1 + r)^n + PMT × ((1 + r)^n − 1) / r = 0

PV is the present value, PMT is the periodic payment, FV is the future value, r is the interest rate per payment period, and n is the number of periods. When payments occur at the beginning of each period, the payment term is multiplied by (1 + r).

If payments and compounding occur at different frequencies, the calculator first converts the annual rate into an effective annual rate and then into a rate per payment period.

What the results include

• Future value: the value at the end of the final period.
• Present value: the value at the start of the plan.
• Periodic payment: the payment made each period.
• Interest rate: the annual nominal rate used by the calculation.
• Periods: the number of payment periods and the equivalent number of years.
• Total payments: the payment amount multiplied by the number of periods.
• Total interest: the difference between the ending value and the cash flows.

Sign convention

The calculator uses a consistent sign convention so that a solution is possible:

• Enter money you receive as a positive number.
• Enter money you pay as a negative number.
• The solved value can be positive or negative, depending on the direction of the cash flow.

If every cash flow has the same sign, there is no internal rate that balances the equation. The calculator will show an error instead of returning a misleading result.

Assumptions and limitations

The model assumes a constant interest rate and equal payments. It does not include fees, taxes, insurance, variable rates, or irregular payment dates. The annual rate is limited to 0% to 100% for this version. Payments per year and compounds per year must be whole numbers from 1 to 365.

Frequently asked questions

What do P/Y and C/Y mean?

P/Y is the number of payments per year. C/Y is the number of times interest compounds per year. They can differ, for example when payments are monthly but interest compounds quarterly.

Why is my payment negative?

A negative payment means money is leaving your account. The sign convention keeps deposits and withdrawals consistent in the equation.

Can I use this for a loan?

Yes. Enter the loan amount as a positive present value, the payment as a negative amount, and the future value as zero. The calculator can then solve for the rate or the number of periods.

What happens at the beginning of a period?

If payments are made at the beginning of each period, each payment has one extra period to earn interest. The calculator adjusts the payment term for this timing.

Source

References:

• Investor.gov — Compound Interest Calculator
• Consumer Financial Protection Bureau — Loans

Disclaimer

This calculator is for informational and educational purposes only. It is not financial advice. Confirm rates, fees, and payment terms with the lender or financial institution before making a decision.