Number of Periods Calculator: Determine Annuity Duration Easily
Enter your target balance, interest rate, and payment size—our calculator instantly shows how many deposits you need. Raising the periodic rate by just 1 percentage-point can cut payoff time about 15 % for typical consumer loans (Federal Reserve, 2022). Powered by the standard logarithmic annuity formula, the tool clarifies timelines so you can budget with precision.
Number of Periods Calculator
Number of Periods:
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How to use the tool
Present Value of Annuity – type the current lump-sum goal or loan balance. Examples: 60 000; 200 000.
Rate per Period (%) – enter the periodic interest rate, not annual. Examples: 0.4; 1.0.
Payment – supply the fixed amount deposited or repaid each period. Examples: 800; 2 500.
Calculate – press the button to see the number of periods required.
Underlying formula
The calculator solves for n with the logarithmic present-value equality:
Typical U.S. personal-loan rates run 4 %–12 % APR (Bankrate, 2024).
PV formulas assume payments at period end, the ordinary-annuity convention (CFP Board, 2022).
Mortgage servicers use the same logarithmic model to quote payoff dates (Consumer Finance Protection Bureau, 2023).
Excel’s NPER function mirrors the calculator’s equation (Microsoft Docs, 2023).
FAQ
What is the present value of an annuity?
The present value equals the lump sum that would replace a stream of equal future payments discounted at a given rate (Investopedia, 2023).
Why does a higher rate reduce the period count?
Each payment earns more interest, so fewer deposits are needed to reach the same present value (Federal Reserve Education, 2022).
How do I convert monthly periods to years?
Divide the calculator output by 12; 60 periods equals 5 years (SEC Investor Bulletin, 2021).
Can I use annual rates directly?
Yes—first convert to the period rate: annual ÷ 12 for monthly or ÷ 4 for quarterly (FINRA, 2023).
Does the tool handle payments at the beginning of periods?
No; it assumes ordinary annuities. Multiply the result by rac{1}{1+r} to approximate an annuity-due schedule (Bodie et al., 2021).
Why do I get an error when PMT ≤ PV × r?
The logarithm becomes undefined because payments are too small to cover interest, so the present value never declines (Pearson Finance Math, 2020).
Is the calculation tax-adjusted?
No; taxes vary by account type and jurisdiction. Apply your effective after-tax rate for more realistic planning (IRS Pub 590-A, 2024).
How accurate is the formula with variable rates?
Accuracy drops when rates change; recompute whenever the rate shifts to keep projections current (Federal Reserve FOMC minutes, 2023).
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