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Engineering Economics — Interest Factors & NPV

Compute all eight standard interest factors for a given rate and number of periods, convert a quoted nominal rate to an effective rate, and evaluate the net present value of any cash-flow series. Enter the effective rate per period — if your rate is nominal, convert it first.

(F/P, i, n) = (1 + i)ⁿ (P/F, i, n) = (1 + i)⁻ⁿ

(F/A, i, n) = [(1 + i)ⁿ − 1]/i (A/F, i, n) = i/[(1 + i)ⁿ − 1]

(P/A, i, n) = [(1 + i)ⁿ − 1]/[i(1 + i)ⁿ] (A/P, i, n) = [i(1 + i)ⁿ]/[(1 + i)ⁿ − 1]

(P/G, i, n) = (1/i){[(1 + i)ⁿ − 1]/[i(1 + i)ⁿ] − n/(1 + i)ⁿ} (A/G, i, n) = (P/G, i, n)·(A/P, i, n)

i_eff = (1 + r/m)^m − 1 NPV = −C₀ + Σ_t=1..n C_t/(1 + i)^t

i is the effective rate per period. The payment period and the interest period must match: monthly payments need a monthly effective rate. The gradient factors assume the series starts at zero in period 1 and grows by G each period.

Interest factors

Effective rate i (% per period) Number of periods n

Nominal → effective rate

Nominal annual rate r (%) Compounding periods per year m

NPV of a cash-flow series

Enter the cash flows starting with the time-0 investment, separated by commas (negative = outflow). The discount rate is the effective rate per period.

Discount rate i (% per period) Cash flows C₀, C₁, … (comma-separated)

For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook.

Worked example: NPV and benefit-cost for a project decision

A drainage improvement costs $50,000 now and delivers $9,000 per year in flood-damage reduction for 8 years. The agency’s MARR is 6%. Should the project be accepted?

Present worth of benefits: (P/A, 6%, 8) = [(1.06)⁸ − 1]/[0.06(1.06)⁸] = 6.20979, so PW_b = 9,000 × 6.20979 = $55,888
NPV = 55,888 − 50,000 = +$5,888 — positive, so the project earns more than the 6% MARR: accept
B/C = 55,888/50,000 = 1.12 > 1 — same verdict

Exam tip: the interest period and the payment period must match. Monthly payments with a quoted annual rate? Convert to a monthly effective rate first — plugging the annual rate into monthly factors is the number-one arithmetic trap.

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Preparing for exam day? The 110-question FE Civil practice exam is a full 5-hour-20-minute rehearsal with detailed solutions.