## Flash Loan Amount In this lesson, we'll derive a simple equation for determining the maximum borrow amount when creating a leveraged position via flash loans. First, let’s define our variables: - B = total borrowed USD - C = total collateral USD - C₀ = initial amount of collateral in USD deposited by user - L = loan to value ratio (LTV) So, the total borrowed divided by the total collateral must be less than or equal to the loan to value ratio. ```solidity B/C ≤ L ``` Now, let's denote F as the flash loan USD amount. Then: ```solidity B = F ``` Next, we will state that Cs is the USD amount of collateral swapped from a flash loan. ```solidity Cs = F ``` This assumes zero slippage on the swap and zero swap fees. Now, we'll rewrite Cs as a multiple of C₀ for some number k: ```solidity Cs = k * C₀ ``` From this point we can rewrite C as: ```solidity C = C₀ + Cs ``` or ```solidity C = C₀ + k*C₀ = (1 + k) * C₀ ``` Now, we can combine all our expressions to solve for F, starting with: ```solidity B/C ≤ L ``` Since B = F, we can rewrite the expression as: ```solidity F/C ≤ L ``` Next, we'll replace the C: ```solidity F/((1 + k) * C₀) ≤ L ``` Then we'll replace F: ```solidity Cs/((1 + k) * C₀) ≤ L ``` Since Cs = k \* C₀, then: ```solidity (k * C₀)/((1 + k) * C₀) ≤ L ``` The C₀ on the top and the bottom cancel out to give us: ```solidity k/(1 + k) ≤ L ``` From there, we can solve for k: ```solidity k ≤ L / (1 - L) ``` Finally, we can express F in terms of k: ```solidity F = Cs ≤ k * C₀ ``` or ```solidity F ≤ (L / (1 - L)) * C₀ ``` This expression gives us the maximum flash loan amount in terms of LTV and the initial collateral amount.