Problem:

You estimate that you will need $647 thousand in 30 years to buy some cybernetic body enhancements, including infrared vision, retractable claws, and expanded brain storage capacity. To achieve your financial goal, you want to make three equal-sized deposits into an account paying a fixed rate of 7.77%. The first deposit will be made right now, the second 10 years from now, and the third 20 years from now.

Required:

Question: What is the size of each deposit you need to make in order to partake of future cybernetic goodness?

Note: Please provide reasons to support your answer.