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The Genius Of Compounding

Warning: nerd math below

Campfire lists APY statistics for all of their pools, farms, and vaults. These calculations are always based on the current advertised rates of the underlying liquidity pools, lending platforms, or other protocols, (also known as the Base Rate), as well as the expected reward token emissions and their current prices as determined by a price oracle like CoinGecko.

Since one of Campfire's main focus is compounding earnings, and because Campfire only compounds rewarded earnings, Campfire needs to mathematically calculate the advertised reward token rate after compounding it. This calculation includes an assumption: Campfire will compound the pool daily. The calculation also reflects that Campfire will be collecting a percentage of the harvested rewards.

To convert an APR to an APY, Campfire will perform the following calculation:
APY = (baseAPR + (((1+(0.8*rewardAPR/365))^365)-1))
For example, a strategy with a 10% base yield, and a 100% reward token yield, should yield the following calculation. Note that we use 0.1 in place of 10% and 1.00 in place of 100%.
APY = (0.1 + (((1+(0.8*1.00/365))^365)-1)) = 1.3236
To convert this to a percentage, multiply by 100. This strategy should return 132.36%. Using $CAMPFIRE has increased your APR from 110% to 132% after fees.
The above calculation assumes daily compounding of your strategy. Some strategies do not compound daily, despite our best efforts. Either the pools do not have enough money in them, or the strategy does not return enough rewards relative to gas costs to justify daily compounding. This is not a bad thing. For lower and medium yielding strategies the difference between daily or weekly compounding is minimal.
To run the calculation again, but with a different frequency for compounding, you should adjust the chosen formula to the following:
APY = (baseAPR + (((1+(0.8*rewardAPR/compoundsPerYear))^compoundsPerYear)-1))

If we assume a strategy is only compounded once a month, we can run the calculation as follows:
APY = (0.1 + (((1+(0.8*1.00/12))^12)-1)) = 1.269
Using the same example as above (a 10% base rate with a 100% rewards rate), we come to the answer of 126.9%.

Compounding Takes Time To Show Significant Results

- Compounding is slow
- Compounding looks linear, until it doesnโt.

A user may complain that the growth of their pool appears linear and not exponential. It is important to recognize that compound growth does not take place overnight, but rather is the result of a slow process that, like gravity, doesnโt stop and gets more powerful the longer you are affected by it. The chart below of a pool expecting 270+% growth over a year demonstrates that process:

Campfire Pool Compounding Graph

For the first five or six months, an exponential compounding (blue) will be difficult to distinguish from linear growth (red). However, once the two diverge, the compounding process speeds up at an increasing rate. Exponential growth requires patience to see results, even for very high APY pools.

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