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$7$ CF$1-10$p Question

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 $$900$ dollar every year forever. However, it will cost you $$10000$ 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 $3\%$ per year and you would pay the developer today. It will take some time for the developer to build the program and so you expect to get your first positive cashflow from the algorithm in two years time.

a$.$ What is the NPV of this investment?

$($answer with two decimals$)$

b$.$ The developer suggest an improvement based on reinforcement learning so that the amount earned by the algorithm would increase with $1\%$ every year. What is the new NPV$?$

$($answer with two decimals$)$