NumberTally Interest Rate Calculator
What return do you actually need? Enter where your money starts, where it must end up, and how long you have — optionally with monthly contributions — and solve for the required annual interest rate.
Advanced options
With contributions, the rate is solved numerically (bisection) instead of with the closed-form formula.
The math behind the answer
Without contributions there is a direct formula: r = (FV ÷ PV)1/years − 1. It is the compound-growth formula rearranged to solve for the rate — the same calculation behind CAGR.
With monthly contributions there is no closed-form solution, because the rate appears both in the lump-sum growth and inside the annuity factor. The calculator uses bisection: it brackets the true monthly rate between a low and high guess, repeatedly halves the interval, and stops when the interval is narrower than 0.000001 (up to 100 iterations). The result is then converted to an effective annual rate.
Is the required rate realistic?
Compare the answer to history: high-yield savings has paid roughly 4–5%, investment-grade bonds 4–6%, and a diversified stock portfolio about 7–10% per year before inflation — with real risk of down years. If the calculator says you need 14%, the honest fixes are saving more, starting earlier, or extending the timeline, not chasing a miracle return.
Frequently Asked Questions
What is the difference between the monthly and annual rate shown?
The monthly rate is the rate applied each month; the annual rate is the effective yearly equivalent: (1 + monthly)12 − 1. Because of compounding, the effective annual rate is slightly higher than 12 × the monthly rate.
Can the required rate be negative or zero?
Yes. If your contributions alone already reach the goal, the required rate is 0% — and if the goal is below what you'd have without any growth, the math returns a negative rate, meaning you could afford to lose a little each year and still make it.
Why solve numerically instead of using a formula?
The equation FV = PV(1+rm)n + PMT·(((1+rm)n − 1)/rm) cannot be rearranged to isolate rm — it is transcendental. Bisection is simple, robust, and guaranteed to converge since the right side grows monotonically with the rate.
Is this the same as CAGR?
Exactly the same idea. CAGR asks "what steady rate turned this start into this end?" — this calculator just lets you add monthly contributions to the question.
Does it account for taxes or inflation?
No — the solved rate is nominal and pre-tax. For a real (inflation-adjusted) target, roughly add expected inflation to the answer, or reduce your future-value goal to today's dollars first.