Financial & Accounting
Variable-Rate Compound Growth Schedule (PRODUCT(1 + Rates) & FVSCHEDULE)
Compound an initial principal across a sequence of changing periodic interest or return rates using PRODUCT(1 + rateRange) and compute cumulative growth and equivalent geometric return.
Compound changing annual or quarterly rates without helper columns
Fixed-rate FV(rate, nper, 0, -pv) assumes the same periodic interest rate every year. When treasury notes, stepped CDs, or multi-year revenue plans apply a different rate in each period r_1, r_2, ..., r_n, the exact terminal value is Principal * (1 + r_1) * (1 + r_2) * ... * (1 + r_n).
Evaluating Principal * PRODUCT(1 + rateRange) computes the exact multi-period compounded balance directly over positive, zero, and negative periodic returns (-100% < r_i) while remaining transparent and auditable.
| Period | Periodic Rate | Gross Factor (1 + r) | Ending Balance ($10,000 Start) |
|---|---|---|---|
| Year 1 | 5.00% | 1.0500 | $10,500.00 |
| Year 2 | 8.00% | 1.0800 | $11,340.00 |
| Year 3 | -2.00% | 0.9800 | $11,113.20 |
| Year 4 | 6.00% | 1.0600 | $11,779.99 |
Terminal Value Across Variable Periodic Rates
Compounds initial principal B2 across periodic rates B3:B6 and guards negative principal or wipeout rates <= -100%.
=IF(OR(B2 < 0, MIN(B3:B6) <= -1), "Invalid Principal or Rate", ROUND(B2 * PRODUCT(1 + B3:B6), 2))Equivalent Constant Annualized Return (Geometric Rate)
Derives the constant per-period compound rate that produces the identical terminal factor over COUNT(B3:B6) periods.
=ROUND(PRODUCT(1 + B3:B6) ^ (1 / COUNT(B3:B6)) - 1, 6)Try the example
Use the original values or change them to test your understanding.