Zoho Sheet RRI: Constant Growth Rate Between Two Values

• 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 RRI reference. Independent high-precision growth calculations; no native Zoho Sheet test.

=RRI(nper; pv; fv)

Supply the number of periods, the starting value and the ending value. No argument is marked optional. Zoho’s reference describes a rate needed to connect those endpoints; it is not a schedule of intermediate payments.

For positive starting and ending values and a positive period count, the compound-growth model is:

rate = (ending / starting)^(1 / periods) - 1

This equation is an independent reconstruction of constant compounding, not a claim about Zoho’s internal algorithm. The examples use explicit semicolon-separated arguments as printed in its help.

Keep the start and end as nonnegative values here. The source explicitly lists #UNKNOWN_ERROR when pv or fv is negative. Do not import an annuity function’s opposite-sign cash-flow convention into RRI. The reference also explicitly states that fv=0 returns -1, or -100%. It does not give a full specification for zero pv or every invalid period count.

Create GrowthRates with Periods, Start, End, Rate and Reconstructed end in A1:E1. Enter A2:C7:

In D2 enter =RRI(A2;B2;C2) and fill through D7. Format D as a percentage if desired; 0.02 then displays as 2%, rather than becoming a different stored rate.

In E2 enter =B2*(1+D2)^A2 and fill through E7. The expected endings are the original C values: 1331,2706.0804,6561,40000,4500,0. Put =E2-C2 in F2 and fill through F7; the exact mathematical residuals are zero. Small displayed residuals in an app need numerical-precision assessment, not forced replacement of the source values.

The first decline case is -10% per period: four factors of 0.9 multiply 10000 to 6561. The zero-ending row uses the explicitly documented exception, with a positive starting value and positive integer periods.

For row 2, enter =(C2/B2)^(1/A2)-1 in H2; expect 0.1. In H3 enter =B2*(1+H2)^A2; expect 1331. This independent formula exposes the ratio and the per-period root.

For a deliberately invalid sign control, enter =RRI(3;-1000;1331) in H5. Zoho documents #UNKNOWN_ERROR for that negative pv. Keep the error control out of numeric totals. The source’s other generic error categories do not identify every possible invalid argument combination.

Create QuarterlyGrowth. Put numeric 2500 in B2 and 0.02 in E2. Put period 0 in A2. In A3 enter =A2+1 and in B3 enter =B2*(1+$E$2). Fill A3:B3 through row 6.

In E3 enter =RRI(4;B2;B6) for 0.02 per quarter. In E4 enter =(1+E3)^4-1 for 0.08243216, or 8.243216% effective annual growth. In E5 enter =4*E3 for 0.08, an annual nominal-rate expression with quarterly compounding. The nominal and effective figures describe different conventions.

If a balance starts at 1000 and ends at 1500 after one period, =RRI(1;1000;1500) gives 0.5. But a separate contribution of 500 at the end could explain the entire increase without investment growth. RRI receives only the two endpoints and period count; it cannot identify or remove that contribution.

Use IRR for an explicitly modeled periodic cash-flow series, or RATE for its payment-based contract, after reading their own sign and timing requirements. Neither is an automatic substitute without the needed inputs.

PDURATION solves for a period count under a constant-rate model. FVSCHEDULE compounds a supplied varying-rate schedule. These examples are illustrations, not forecasts or statements about fees, taxes or a particular investment.