# Getting Started

Introduction to the DeFiPIE lending protocol

## Introduction

The DeFiPIE protocol is a series of interest rate pools running on a variety of blockchains. When users and applications deposit their assets to the DeFIPIE Protocol, they begin earning a variable interest rate instantly. Interest accrues every block (for Ethereum ~13 seconds, for Binance Smart Chain ~3 seconds), and users can withdraw their principal plus interest anytime.

On the other hand, users can borrow tokens from the pool by paying an interest rate to all pool lenders

When users deposit assets, they receive pTokens from DeFiPIE in exchange. pTokens are ERC20 tokens that can be redeemed for their underlying assets at any time. As interest accrues to the assets deposited, pTokens are redeemable at an exchange rate (relative to the underlying asset) that constantly increases over time, based on the rate of interest earned by the underlying asset.

## Networks

The DeFiPIE Protocol is currently deployed on the following networks:

## Protocol Math

The DeFiPIE protocol contracts use a system of exponential math, Exponential.sol, in order to represent fractional quantities with sufficient precision.

Most numbers are represented as a mantissa, an unsigned integer scaled by 1 * 10 ^ 18, in order to perform basic math at a high level of precision.

### pToken and Underlying Decimals

Prices and exchange rates are scaled by the decimals unique to each asset; pTokens are ERC-20 tokens with 8 decimals In most cases (there are several pTokens exceptions in Ethereum network with 18 decimals), while their underlying tokens vary, and have a public member named decimals.

pTokens exceptions in Ethereum network:

### Interpreting Exchange Rates

The pToken Exchange Rate is scaled by the difference in decimals between the pToken and the underlying asset.

``onePTokenInUnderlying = exchangeRateCurrent / (1 * 10 ^ (18 + underlyingDecimals - pTokenDecimals))``

Here is an example of finding the value of 1 pPIE in PIE with Web3.js JavaScript.

``````const underlying = new web3.eth.Contract(erc20Abi, pieAddress);
const pToken = new web3.eth.Contract(pTokenAbi, pPieAddress);
const underlyingDecimals = await underlying.methods.decimals().call();
const pTokenDecimals = await pToken.methods.decimals().call();
const exchangeRateCurrent = await pToken.methods.exchangeRateCurrent().call();
const mantissa = 18 + parseInt(underlyingDecimals) - parseInt(pTokenDecimals);
const onePTokenInUnderlying = exchangeRateCurrent / Math.pow(10, mantissa);
console.log('1 pPIE can be redeemed for', onePTokenInUnderlying, 'PIE');``````

There is no underlying contract for ETH and BNB, so to do this with pETH and pBNB, set underlyingDecimals to 18.

To find the number of underlying tokens that can be redeemed for pTokens, multiply the number of pTokens by the above value onePTokenInUnderlying.

``underlyingTokens = pTokenAmount * onePTokenInUnderlying``

### Calculating Accrued Interest

Interest rates for each pool update on any block in which the ratio of borrowed assets to deposited assets in the pool has changed. The amount interest rates are changed depends on the interest rate model smart contract implemented for the pool, and the amount of change in the ratio of borrowed assets to deposited assets in the pool.

Interest accrues to all lenders and borrowers in a pool when any Ethereum address interacts with the poolâ€™s pToken contract, calling one of these functions: mint, redeem, borrow, or repay. Successful execution of one of these functions triggers the accrueInterest method, which causes interest to be added to the underlying balance of every lender and borrower in the pool. Interest accrues for the current block, as well as each prior block in which the accrueInterest method was not triggered (no user interacted with the pToken contract). Interest compounds only during blocks in which the pToken contract has one of the aforementioned methods invoked.

Here is an example of supply interest accrual:

Alice deposits 1 ETH to the DeFiPIE protocol. At the time of deposit, the supplyRatePerBlock is 37893605 Wei, or 0.000000000037893605 ETH per block. No one interacts with the pEther contract for 3 Ethereum blocks. On the subsequent 4th block, Bob borrows some ETH. Aliceâ€™s underlying balance is now 1.000000000151574420 ETH (which is 37893605 Wei times 4 blocks, plus the original 1 ETH). Aliceâ€™s underlying ETH balance in subsequent blocks will have interest accrued based on the new value of 1.000000000151574420 ETH instead of the initial 1 ETH. Note that the supplyRatePerBlock value may change at any time.

### Calculating the APY Using Rate Per Block

The Annual Percentage Yield (APY) for lending or borrowing in each pool can be calculated using the value of supplyRatePerBlock (for deposit APY) or borrowRatePerBlock (for borrow APY) in this formula:

``````Rate = pToken.supplyRatePerBlock(); // Integer
Rate = 37893566
ETH Mantissa = 1 * 10 ^ 18 (ETH has 18 decimal places)
Blocks Per Day = 4 * 60 * 24 (based on 4 blocks occurring every minute)
Days Per Year = 365

APY = ((((Rate / ETH Mantissa * Blocks Per Day + 1) ^ Days Per Year)) - 1) * 100``````

Here is an example of calculating the deposit and borrow APY with Web3.js JavaScript:

``````const ethMantissa = 1e18;
const blocksPerDay = 4 * 60 * 24;
const daysPerYear = 365;

const pToken = new web3.eth.Contract(pEthAbi, pEthAddress);
const supplyRatePerBlock = await pToken.methods.supplyRatePerBlock().call();
const borrowRatePerBlock = await pToken.methods.borrowRatePerBlock().call();
const depositApy = (((Math.pow((supplyRatePerBlock / ethMantissa * blocksPerDay) + 1, daysPerYear))) - 1) * 100;
const borrowApy = (((Math.pow((borrowRatePerBlock / ethMantissa * blocksPerDay) + 1, daysPerYear))) - 1) * 100;
console.log(`Deposit APY for ETH \${depositApy} %`);
console.log(`Borrow APY for ETH \${borrowApy} %`);``````

Last updated