You have developed an algorithm based on Artificial Intelligence that trades foreign exchange automatically using statistical arbitrage. You expect that the algorithm will give you a small but steady profit of $500 dollar every year forever. However, it will cost you $8 000 today to hire a developer who can set up the program. You want to know whether you should go through with this idea. The interest rate is 2.5% per year and you would pay the developer today and expect to get your first $500 dollar from the algorithm in two years time.

a. What is the NPV of this investment? Answer in dollar amount with two decimals (i.e. 230.04). $

b. The developer suggest an improvement based on reinforcement learning so that the amount earned by the algorithm would increase with 1.5% every year. What is the new NPV? Answer in dollar amount with two decimals (i.e. 230.04). $

c. You consider whether you should learn to code so that you can build the program that supports the trading algorithm yourself. You would study part-time for the coming 5 years, but would then be able to build the algorithm for free (including the improvement suggested by the developer). Your first profit from the algorithm is thus expected in 6 years. What is the new NPV?