Calculating Probability

I need to calculate the expected cost of an event that may occur at anytime during a 5 year period. The event occurrence has an annual probability of 10%. If the event occurs in Year 1 - the costs incurred will be the annual payment amount ($10,000) multiplied by 5. If the event occurs in Year 2 - the costs incurred will be the annual payment amount ($10,000) multiplied by 4 etc etc. I want to know, given an annual probability of 10% what is the probability of an event occurring during the 5 year period. I also need to know what is the expected cost of that event. You will need to show workings so that i can change the annual probability and payment amount.