Zoho Sheet PDURATION: Periods to Reach a Compound-Growth Target

• Introduced: Original introduction release and date are not established by the checked sources.
• Availability: Currently documented in Zoho Sheet’s rolling web-service help; no retirement endpoint is established.
• Scope: English web-service documentation. Exact mobile and offline-client parity is unverified.
• Checked: October 14, 2026, against the official PDURATION reference. Independent high-precision growth calculations; no native Zoho Sheet test.

=PDURATION(rate; present_value; future_value)

All three inputs are supplied. The rate is per period, and the result counts the same kind of period. Use 0.05 or 5% for a five-percent rate, not the plain number 5. No payment, calendar-date, timing or guess argument is documented.

The checked page lists a general #NUM! description for invalid values but does not define every boundary. These examples deliberately use positive rates, positive starting values and larger positive targets. Zero/negative-rate, zero-start, and shrinking-target cases are not assigned invented native errors or results.

For this positive growth domain, independently solve the compound-value equation using:

periods = LN(target / start) / LN(1 + rate)

The logarithmic expression is a mathematical cross-check. It is not a disclosed description of the function’s implementation.

Create GrowthPeriods with Rate, Start, Target, Periods and Reconstructed target in A1:E1. Enter:

Enter =PDURATION(A2;B2;C2) in D2 and fill through D6. Except for the exact three-period row, the displayed expectations are rounded to ten decimal places.

In E2 enter =B2*(1+A2)^D2 and fill through E6. Expect 1331,3000,1500,5000,5000 using the unrounded period results. In F2 enter =LN(C2/B2)/LN(1+A2) and fill through F6; the expected period counts match D.

Rows 5 and 6 intentionally distinguish 12.3% from the numeric literal 12.3, which is a 1230% rate. Both are mathematical positive-rate inputs, but they produce radically different growth factors, 1.123 and 13.3. Zoho’s argument example prints 12.3; do not silently read that number as 12.3%.

The eight-and-a-fraction result in row 3 solves an exponential equation. It is not a claim that a real account credits a fraction of a period, nor a promise that a target is reached after only eight completed periods.

If the illustrative model credits growth only at whole period ends, round the required count upward. On a separate TargetSchedule, put period 0 in A2 and starting value 2000 in B2. Put rate 0.05 in E2 and target 3000 in E3.

In A3 enter =A2+1; in B3 enter =B2*(1+$E$2). Fill A3:B3 through row 11 to calculate periods one through nine.

In E4 enter =PDURATION(E2;B2;E3) for approximately 8.3103862225. In E5 enter =ROUNDUP(E4;0) for 9. B10, the balance after eight periods, is below the target; B11, after nine periods, is above it. This consecutive-balance check verifies the whole-period interpretation without claiming an actual crediting policy.

Create MonthlyTarget with 0.01 in B2, 1000 in B3 and 1500 in B4. In B5 enter =PDURATION(B2;B3;B4); expect approximately 40.7489071561 months if B2 is a monthly rate. In B6 enter =B5/12; expect approximately 3.3957422630 years as a conversion of that mathematical time count.

In B7 enter =(1+B2)^12-1; expect 0.1268250301, approximately, for the effective annual rate. In B8 enter =PDURATION(B7;B3;B4); expect the same 3.3957422630 years as B6. Using a simple 12% annual figure instead would specify a different compounding model.

The model contains no additional deposits, withdrawals, fees or taxes. NPER has a payment-based contract; RRI solves for the constant rate between endpoints. FVSCHEDULE applies an explicit sequence of rates, while LN and ROUNDUP support the transparent checks here.

These are independently calculated scenarios, not investment forecasts. Do not assign exact malformed-input errors or cross-client parity beyond the checked source. Preserve unrounded calculated periods when reconstructing the target, and distinguish formula precision from display formatting.