Interest Rate Calculator
Work backward from a starting amount and an ending amount to find the interest rate that connects them. Enter both amounts, a time frame, and a compounding frequency to see the exact rate you'd need.
Your required rate will appear here
Enter your starting and ending amounts and the time frame, then click calculate.
Quick Answer
To find the rate needed for a lump sum to grow from P to A over t years, use r = n x [(A/P)^(1/(n x t)) - 1]. For $5,000 growing to $6,500 in 5 years compounded annually, that works out to about 5.39% a year, noticeably lower than the 6.00% simple rate the same growth would imply.
How It Works: Formula & Variables
r = n × [(A/P)^(1/(n·t)) − 1]
- P (Start)
- The amount you started with.
- A (End)
- The amount you ended with, or want to reach.
- t (Time)
- The number of years between the two amounts.
- n (Frequency)
- How often the rate compounds per year.
Simple-interest version, if the growth wasn't compounded at all: r = I / (Pt), where I = A − P.
Sources: SEC, Investor.gov on the annual rate of return and the Investor.gov Compound Interest Calculator, which this reverses.
Worked Examples
Example: $5,000 growing to $6,500 in 5 years
Compounded annually: r = (6,500/5,000)^(1/5) − 1 = 5.39% a year. If the same growth happened with simple interest instead: r = (6,500 − 5,000) / (5,000 × 5) = 6.00%. The compound rate is lower because compounding is doing part of the work.
Key Concepts
A rate is always tied to a compounding schedule: Saying "I need a 6% return" means nothing on its own until you know whether that's simple, or compounded annually, monthly, or some other way.
This is essentially CAGR for a single deposit: With no extra contributions along the way, solving for the compound rate here gives you the same number an investor would call the compound annual growth rate.
Comparing to an advertised APY takes an extra step: A rate you calculate here isn't directly comparable to a bank's APY until you run it through APY = (1 + r/n)^n − 1.
Common Mistakes
Using the simple-rate shortcut for compounded growth: Dividing profit by principal and by years gives the simple rate, not the compound rate, and the two can differ by a full percentage point or more.
Forgetting that periodic deposits break the formula: The moment you add regular contributions on top of a starting balance, this direct formula no longer applies, and the rate has to be solved for through trial and error instead.
Skipping annualization: A rate calculated over a 3-year or 5-year stretch needs to be expressed per year to be useful for comparison, which is exactly what this formula already does.
Frequently Asked Questions
Use r = n x [(A/P)^(1/(n x t)) - 1], where P is the starting amount, A is the ending amount, t is the number of years, and n is how often the rate compounds. Enter your two amounts and the time frame, and the calculator solves it for you.
Because the rate needed to hit a given ending amount depends on how often that rate compounds. A lower monthly-compounded rate and a higher annually-compounded rate can produce the exact same ending balance.
For a single lump sum with no additional deposits along the way, yes. What this calculator returns with annual compounding (n = 1) is the compound annual growth rate.
The simple rate is always higher for the same amount of growth, since compounding does some of the work for you. On $5,000 growing to $6,500 over 5 years, the compound rate is 5.39% while the simple rate works out to 6.00%.
No. This formula solves for the rate on a single lump sum with no extra contributions added in between. Once you add periodic deposits, there's no closed-form formula, and the rate has to be found through iteration instead.
The underlying formula returns a decimal. This calculator already multiplies by 100 and shows you a percentage, so no extra conversion is needed on your end.
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