Financial & Accounting
PDURATION & RRI Formulas: Periods to Reach Target Value & Equivalent Return
Calculate the exact number of compounding periods required for an investment to grow from PV to FV (PDURATION) and the equivalent compound growth rate over N periods (RRI) using exact logarithmic and power identities.
Exact closed-form identities behind PDURATION and RRI
Starting from the lump-sum compounding equation FV = PV * (1 + r)^n (with zero intermediate cash flows), taking natural logarithms solves directly for the required number of periods: n = LN(FV / PV) / LN(1 + r), which is the exact mathematical definition of Excel’s PDURATION(rate, pv, fv).
Solving the same equation for r over a known horizon n yields r = (FV / PV)^(1 / n) - 1, which is Excel’s RRI(nper, pv, fv). Unlike IRR or NPER, these two closed-form expressions require no iterative solver, never fail to converge, and evaluate identically across every spreadsheet engine.
| Scenario | Present Value (PV) | Target Value (FV) | Rate / Horizon | Exact Result |
|---|---|---|---|---|
| Double capital at 8% annual | $10,000 | $20,000 | r = 8.00% / yr | 9.0065 years (PDURATION) |
| Grow 50% at 0.5% / month | $10,000 | $15,000 | r = 0.50% / mo | 81.2956 months (PDURATION) |
| Double capital in 10 years | $10,000 | $20,000 | n = 10 years | 7.1773% / yr (RRI) |
| Grow $10k to $18,509.30 in 8 yrs | $10,000 | $18,509.30 | n = 8 years | 8.0000% / yr (RRI) |
Exact Periods to Reach Target Value (PDURATION Identity)
Computes LN(FV / PV) / LN(1 + rate) while guarding non-positive PV, FV, or rate.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Input", ROUND(LN(B3 / B2) / LN(1 + B4), 4))Equivalent Compound Growth Rate Over N Periods (RRI Identity)
Computes (FV / PV)^(1 / nper) - 1 for horizon B5 > 0 and positive PV (B2) and FV (B3).
=IF(OR(B2 <= 0, B3 < 0, B5 <= 0), "Invalid Input", ROUND((B3 / B2) ^ (1 / B5) - 1, 6))Try the example
Use the original values or change them to test your understanding.