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?
2 Answers
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? Dec 23, 2021 at 16:49
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1Number of years. If you use compounding period other than years you'd need to adjust the formula slightly. Dec 23, 2021 at 16:50
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2Note 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. Dec 23, 2021 at 17:57 -
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1Technically, it’s continuous growth. That’s great for a lot of things, but not finance.– RonJohnDec 23, 2021 at 18:19
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What about estimating APY for a stock portfolio? Would that be continuous growth? Dec 23, 2021 at 23:36
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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".– dreevesDec 24, 2021 at 0:56