Periodic Payment

Purpose

This calculator solves for the fixed payment made at regular intervals that reconciles a starting amount, a target ending amount, and an interest rate — the same calculation behind loan installments, mortgage payments, or regular contributions needed to reach a savings goal. It is useful whenever you know the present and future amounts involved and need to find the regular payment that connects them.

Background

One payment, many uses

The same formula answers very different questions depending on how you set the inputs. Set Future Value to 0 and treat Present Value as money you receive (a loan) to find a loan installment. Set Present Value to 0 and give a target Future Value to find the regular contribution needed to reach a savings goal. Mixing a nonzero Present Value and Future Value finds the payment needed to bridge between a starting and ending amount over the Duration, at the given Interest Rate.

Direction of cash flows

Both Present Value and Future Value are marked as either Incoming (money you receive) or Outgoing (money you pay), using the Present Value Direction and Future Value Direction settings. The calculated Periodic Payment is always shown as a positive amount, with a separate Cash Flow result telling you whether that payment is money you would pay (Outgoing) or receive (Incoming), based on the combined directions of what you entered.

Inputs

Present Value

The amount at the start of the Duration.

Present Value Direction

Whether the Present Value is Outgoing (money you pay or invest) or Incoming (money you receive, such as loan proceeds).

Future Value

The amount at the end of the Duration.

Future Value Direction

Whether the Future Value is Incoming (money you will receive) or Outgoing (money you will owe or pay).

Interest Rate

The annual nominal interest rate that applies throughout the Duration (for example, 6 pct/yr). It is converted internally to a rate per Payment Interval.

Duration

The total length of time from the Present Value to the Future Value (for example, 5 yr). Together with Payment Interval, this determines the number of payments.

Payment Interval

How often payments are made (for example, every month).

Payment When

Whether each payment is made at the Period Start (an annuity due) or the Period End (an ordinary annuity, the usual convention for loan installments).

Results

Periodic Payment

The fixed amount to be paid or received at every Payment Interval that reconciles the Present Value growing (or being paid down) to the Future Value over the Duration, at the given Interest Rate. Always shown as a positive amount.

Cash Flow

States whether the Periodic Payment is money Outgoing (you would pay it each period) or Incoming (you would receive it each period), based on the combined direction of the Present Value and Future Value you entered.

Understanding the Calculation

The annual Interest Rate is converted to a rate per Payment Interval, and the number of payments is Duration divided by Payment Interval. The Periodic Payment is then the fixed payment amount that satisfies the standard time-value-of-money relationship linking a present value, a future value, and a series of equal payments, given whether each payment falls at the start or end of its period (Payment When). Present Value and Future Value are treated as signed amounts (positive if Incoming, negative if Outgoing) when solving for the payment.

Example

Using the default inputs — a Present Value of 100,000 (Outgoing), a Future Value of 200,000 (Incoming), an Interest Rate of 6% per year, a Duration of 5 years, paid monthly at the start of each month — the calculator finds a Periodic Payment of approximately 928.64, with Cash Flow shown as Outgoing.

As a loan example: borrowing 100,000 (Incoming to you) at 6% per year over 5 years, to be fully repaid (Future Value of 0) with equal payments at the end of each month, gives a Periodic Payment of approximately 1,933.28, shown as Outgoing — the familiar monthly installment for that loan.

Important Assumptions and Interpretation

• Interest Rate is assumed constant, and payments are assumed equal and evenly spaced, for the entire Duration.
• Getting Present Value Direction and Future Value Direction right matters for interpreting Cash Flow correctly, even though Periodic Payment itself is always reported as a positive number.
• The result is a calculated payment based on the assumed constant rate; it does not include fees, taxes, or changes to the rate over time.