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I'm having trouble figuring out the formula for calculating APY given a starting balance, ending balance, and term in length of years. What's the formula to do this?

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The formula for APY is essentially solving the future value (or present value) formula for the rate:

    end_bal = start_bal * (1+APY)^N
==> (1+APY)^N = (end_bal/start_bal)
==> 1+APY = (end_bal/start_bal)^(1/N)
==> APY = (end_bal/start_bal)^(1/N) - 1
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  • Thank you! And am I correct to assume that N is number of periods?
    – Nathan Arthur
    Dec 23, 2021 at 16:49
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    Number of years. If you use compounding period other than years you'd need to adjust the formula slightly.
    – D Stanley
    Dec 23, 2021 at 16:50
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I decided to go with the solution a friend gave me, since it gives me continuous compounding:

enter image description here

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    Note that your result is not exactly the APY. APY assumes annual compounding, not continuous. But you could easily convert your answer to annual compounding: APY = e^r - 1. Mathematically it ends up the same.
    – D Stanley
    Dec 23, 2021 at 17:57
  • What would what I have be considered technically?
    – Nathan Arthur
    Dec 23, 2021 at 18:05
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    Technically, it’s continuous growth. That’s great for a lot of things, but not finance.
    – RonJohn
    Dec 23, 2021 at 18:19
  • What about estimating APY for a stock portfolio? Would that be continuous growth?
    – Nathan Arthur
    Dec 23, 2021 at 23:36
  • I think continuous is the right answer to the question "what is the effective APY for an investment that went from $a to $b in t years".
    – dreeves
    Dec 24, 2021 at 0:56

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