RATE Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this is a verified release, not a final supported version.
• Scope: Desktop Calc, English function names and semicolon-separated formulas.
• Checked: October 14, 2026. Eight ordinary reference formulas were recalculated from generated ODF in 4.1.16 on Linux x86-64, Build 9816. Source and independent arithmetic were checked.

RATE finds an interest rate per payment period for a constant-payment financial arrangement. It solves the payment and balance equation rather than dividing total interest by principal. Its sign convention requires consistent incoming and outgoing amounts. Release implementation.

=RATE(Nper;Payment;PV[;FV[;Type[;Guess]]])

• Nper: positive number of equal payment periods.
• Payment: constant signed payment each period.
• PV: signed present value.
• FV: optional final balance, default 0.
• Type: optional 0 for payments at the end; use 1 for payments at the beginning.
• Guess: optional initial rate, default 0.1.

The native column contains saved 4.1.16 results; independent references use high-precision arithmetic and the stated source rules. Values are shown to twelve decimal places where needed.

Twelve end-of-period payments of −100 against a present loan value of 1000 imply approximately 0.029228540769 per period. Moving the payments to the beginning, while keeping their amount and number unchanged, gives approximately 0.035031530362. Earlier payments support a higher rate for the same present amount.

If those periods are months, the first result is a monthly rate. A nominal annual rate formed by multiplying by twelve differs from the effective annual rate (1+r)^12-1. State which conversion is being reported; RATE does not assign a calendar unit itself.

For r≠0, check PV*(1+r)^Nper+Payment*(1+r*Type)*((1+r)^Nper-1)/r+FV. The residual should be near zero for the proposed rate. The zero-rate limiting equation is PV+Payment×Nper+FV=0.

With no intervening payments, a present outflow −100 growing to 200 in ten periods gives 2^(1/10)-1, approximately 0.071773462536. Similarly, −100 growing to 161.051 over five periods implies 10%. These independent compounding identities are useful checks of sign and time-unit choices.

The source rejects Nper≤0 and uses an iterative solver with a maximum of 150 iterations. Integer and noninteger Nper take different solver branches; the native examples here use positive integer counts and positive roots. No global convergence or extreme-value claim follows from them.

Use Type 0 or 1. Unlike the payment helper’s positive/nonpositive timing branch, RATE’s solver algebra retains the supplied Type value; arbitrary flags should not be substituted casually. A poor guess or a cash-flow equation without a suitable root can prevent convergence. Invalid-domain and unsuccessful searches were not executed.

PMT, NPER, FV.

• Function-specific release implementation
• RateIteration calculation

The generated ODF produced the informational load warning “Not all attributes could be read.” The sheet was hard-recalculated and saved separately. All eight ordinary function identities, inputs and results were reconciled; a stale SUM cache changed from 999999 to 3 and an uncached SUM returned 7. This establishes the stated examples, not every workbook style or invalid input. Other explanatory identities are independent calculations. The authoring-tool XLSX was not executed in OpenOffice, and its preview values are not the native results reported here.