Zoho Sheet FVSCHEDULE: Future Value with Changing Interest Rates

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

=FVSCHEDULE(principal; interest_rates)

Supply the initial value and a range or array containing the rate schedule. No recurring-payment argument is documented. Zoho expressly permits blank cells in the rate range, but the short text does not explain every blank or empty-string context. The main example uses four explicit numeric rates; a separate control uses a real zero rate rather than relying on a blank.

Enter five percent as 0.05 or 5%. The compounding model multiplies the principal by every factor 1+rate. Negative rates in the example represent a decline in one period; all displayed factors remain positive. Rates at or below -100%, imported text, errors and negative-principal boundaries are not inferred from this fixture.

The formula models a supplied sequence, not a forecast of future rates. Period definitions must be consistent with the rates you enter.

Create RateSchedule, with Rate, Growth factor and Closing balance in A1:C1. Put Principal in D1 and numeric 10000 in D2. Enter 0.05,0.02,0.03,-0.01 in A2:A5.

Put =1+A2 in B2 and fill through B5. In C2 enter =$D$2*B2. In C3 enter =C2*B3 and fill through C5.

In F2 enter =FVSCHEDULE(D2;A2:A5); expect 10920.987. In F3 enter =D2*B2*B3*B4*B5; expect the same value. In F4 enter =F2-C5; the exact mathematical difference is 0.

This recurrence makes the input timing explicit: no new contribution is inserted between periods. A deposit or withdrawal would need a separate model rather than being hidden in the interest-rate cells.

Create TwoRates. Put numeric 50000 in D2 and rates 0.4,0.25 in A2:A3. In F2 enter =FVSCHEDULE(D2;A2:A3); expect 87500, from 50000×1.4×1.25.

The inline array form =FVSCHEDULE(50000;{0.4;0.25}) gives the same independently expected result and follows the array notation in Zoho’s first example. Its published reference-cell example also shows 87500; the inputs here are fully specified rather than depending on an unseen A2 value.

On a separate ZeroRatePeriod sheet, enter rates 0.05,0,0.02 in A2:A4 and principal 1000 in D2. In F2 enter =FVSCHEDULE(D2;A2:A4); expect 1071. The successive balances are 1050,1050,1071. A numeric zero supplies the factor one; it is not an observation about a formula returning empty text.

Copy RateSchedule to ReverseSchedule and replace A2:A5 with -0.01,0.03,0.02,0.05. The existing factor and balance formulas recalculate.

Expected C2:C5 is 9900,10197,10400.94,10920.987. F2:F3 still give 10920.987, and F4 remains zero in exact arithmetic.

Multiplication of the same four growth factors has the same product regardless of order. Intermediate balances differ because each partial product contains a different subset. This endpoint property assumes there are no intervening cash flows or balance-dependent rules; with those additions, order can matter to the final result too.

Return to the original RateSchedule. In H2 enter =AVERAGE(A2:A5) for 0.0225, or 2.25%. In H3 enter =D2*(1+H2)^4; expect 10930.833187890625. In H4 enter =H3-F2; expect 9.846187890625.

The arithmetic average describes the four rates but does not reproduce their product. In H5 enter =RRI(4;D2;F2) for approximately 0.0222696624. In H6 enter =D2*(1+H5)^4; expect 10920.987 using H5’s unrounded result. This is the constant per-period rate equivalent to this schedule’s endpoint.

The generic error list does not settle every malformed schedule, blank representation or extreme rate. Use explicit numeric rates when testing a transferred workbook and distinguish number formatting from stored values. The separate positive principal and varying-rate model here does not establish an annuity sign convention.

FV has a constant-rate, payment-based contract. RRI connects endpoints with a constant rate, and PDURATION solves for time. AVERAGE explains the arithmetic mean used in the contrast.