Google Sheets - formula for expense sheet - if-statement

Question

I need a formula that will help me calculate the $ expense amount for my milage rates.
Here is my sheet https://docs.google.com/spreadsheets/d/1PPFuFWbxWi9iIdtYBJvnSNB1j1cjjQutepF3hnpGoFM/edit?usp=sharing
On the tab that's expenses, I need to check the year of my date in Col A (because different years have different rates), then check Col D to see if it says Milage, then check Col E for what type of milage (there are 4 types), then return the number input in Col I times the appropriate rate for that year and type of milage. I have a table set up with the rates in another tab.
I'm thinking it will be a long IF and AND formula. Any help would be great!

Answer 1

In 'Essentials Log', I've changed the format of your year start-end dates to state the year you're referencing. I've added a column for "Milage".
Expense Reference Screenshot
In 'Expenses'!M2, I tried this and it seems to work:
=ARRAYFORMULA(iferror(if(isblank(A2:A),"",I2:I*vlookup(D2:D&year(A2:A)&E2:E,query({'Essentials Log'!Y2:Y&'Essentials Log'!Z2:Z&'Essentials Log'!AA2:AA,'Essentials Log'!AB2:AB},"Select *"),2,false))))
Working Example Screenshot
Have a look (I copied your example sheet): Milage expense

Answer 2

I solved this with creating an app script.
I realized I didn't want to use a formula because in my $ col most entries will be keyed in and so I didn't want to copy and paste a formula every time.
Here is the code if anyone might need it. I added it to the menu so the calculation is done with a click.
function expenseMilageCalculation() {
var auditionsSheet = SpreadsheetApp.getActiveSpreadsheet();
var expensesTab = auditionsSheet.getActiveSheet();
var activeCell = expensesTab.getActiveCell();
var activeRow = activeCell.getRow();
var expenseDate = expensesTab.getRange(activeRow, 1).getValue();
var expenseYear = expenseDate.getFullYear();
var expenseType = expensesTab.getRange(activeRow, 4).getValue();
var expenseDetails = expensesTab.getRange(activeRow, 5).getValue();
var numMiles = expensesTab.getRange(activeRow, 9).getValue();
var essentialsLogTab = auditionsSheet.getSheetByName("Essentials Log")
//2018 Business Milage
if (expenseYear == 2018 && expenseType == "Milage" && expenseDetails == "Business") {
var milageBusinessRate2018 = essentialsLogTab.getRange(3, 27).getValue();
var dollarMilesDeduction = numMiles * milageBusinessRate2018
expensesTab.getRange(activeRow, 8).setValue(dollarMilesDeduction)
}
//2019 Business Milage
if (expenseYear == 2019 && expenseType == "Milage" && expenseDetails == "Business") {
var milageBusinessRate2019 = essentialsLogTab.getRange(8, 27).getValue();
var dollarMilesDeduction = numMiles * milageBusinessRate2019
expensesTab.getRange(activeRow, 8).setValue(dollarMilesDeduction)
}