Use Lookup formula to calculate total costings

Hello Everyone,
I hope you can help.
I have (hopefully) attached an excel file that shows the basic idea of what I am trying to do. In the first sheet I have a column for year and next to that I want the total costing for the year. In the second sheet I have a column for the year, the change number, the description of the change and the cost. I want a formula to look at this table array find the rows with the a certain year, calculate the total (sum them up) and put that figure in the first sheet.

Hope you were able to follow that
Cost of changes.xlsx

Hello Richard,

This works brilliantly in the attached sheet, I'll try on the main one now. Thank you.