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Payback Period Calculator

Computes how long an investment takes to recover its initial outlay from a list of periodic cash flows or a constant annual cash flow, both undiscounted (simple payback) and discounted at a given rate (discounted payback), interpolating within the recovery period.

When to use

You want a quick liquidity/risk measure of a project: the years until cumulative cash inflows equal the initial investment.

Do not use when: You need the value created over the whole life (use npv) or the rate of return (use irr); payback ignores cash flows after recovery.

Formula

Simple: payback = (k − 1) + (initial_investment − cumulative_{k−1}) / CF_k, where k is the first period with cumulative ≥ initial_investment. Discounted: same with CF_t / (1 + r)^t. Constant flow: payback = initial_investment / annual_cash_flow.

Cash flows arrive at the end of each period but the fractional part assumes they accrue evenly within the recovery period. Payback ignores cash flows after recovery and (in the simple form) the time value of money.

Inputs

Parameter	Type	Unit	Required	Description
`initial_investment`	number		yes	Outlay at time 0, entered as a positive number. Range: > 0, ≤ 1000000000000000
`cash_flows`	number_list		no	Net cash inflow at the end of each period; takes precedence over annual_cash_flow.
`annual_cash_flow`	number		no	Used with `years` when cash_flows is omitted. Range: > 0, ≤ 1000000000000000
`years`	integer	years	default 20	Length of the constant cash-flow series (ignored when cash_flows is given). Range: ≥ 1, ≤ 60
`discount_rate_percent`	number	% per period	default 0	Rate for the discounted payback; 0 skips it. Range: ≥ 0, ≤ 100

Outputs

Output	Type	Unit	Description
`payback_period_years`	number	periods	Periods until cumulative undiscounted cash flow reaches the investment, interpolated within the final period.
`payback_time`	string		payback_period_years expressed in years and months.
`discounted_payback_period_years`	number	periods	Same using cash flows discounted at discount_rate_percent (only when the rate is > 0).
`payback_reached`	boolean		False when the cash flows never add up to the investment.
`cumulative_cash_flows`	number_list		Running total of undiscounted cash flows after each period.
`total_cash_flows`	number		Σ cash flows over the series.

Example

10,000 then 3,000, 4,000, 5,000, 2,000 at 8 %: {"initial_investment":10000,"cash_flows":[3000,4000,5000,2000],"discount_rate_percent":8} → {"payback_period_years":2.6,"payback_time":"2 years 7 months","discounted_payback_period_years":2.96,"payback_reached":true,"cumulative_cash_flows":[3000,7000,12000,14000],"total_cash_flows":14000}

50,000 with 12,000 per year for 10 years at 10 %: {"initial_investment":50000,"annual_cash_flow":12000,"years":10,"discount_rate_percent":10} → {"payback_period_years":4.17,"discounted_payback_period_years":5.67,"payback_reached":true}

GET https://tttkmbb.com/api/v1/calculate/payback-period?initial_investment=10000&cash_flows=3000%2C4000%2C5000%2C2000&discount_rate_percent=8

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/payback-period (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/payback-period · Markdown: https://tttkmbb.com/finance/payback-period.md · JSON definition: https://tttkmbb.com/finance/payback-period.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="payback-period"
OpenAPI operationId: calculate_payback_period
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Investopedia – Payback Period: Definition, Formula and How to Calculate (reference)
Investopedia – Discounted Payback Period (reference)
Wikipedia – Payback period (reference)

FAQ

Why is the discounted payback longer?

Discounting shrinks later cash flows, so it takes more of them to add up to the investment: 2.96 instead of 2.6 years in the example at 8 %.

What if the investment is never recovered?

payback_reached is false and the payback outputs are omitted; the cumulative list shows how far the cash flows get.

Related calculators

NPV Calculator — Value of all cash flows, including those after payback.
IRR Calculator — Rate of return of the same cash flows.
Break-Even Calculator — Units needed to cover fixed costs.