Present value X71853

Dessign the function @valor_presente(I, r)@ that calculates the present value of an investment $I$ represented as a list of monthly payments and a monthly interest rate $r$.

Example: John asks Paul to rent his vehicle for 3 months for a monthly payment of 5000 euros (the first payment is today). Once this time has passed, he will buy the vehicle for 45000 euros. John’s opportunity cost is 5% monthly. ¿Which is the present value of the project?

John’s investment is: $I= [5000, 5000, 5000, 45000]$. The opportunity cost is $r = 0.05$. The @valor_presente(I, r)@ is $$5000 + 5000/(1.05) + 5000/(1.05)^2 + 45000/(1.05)^3 = 53169.74408811143$$

In general, if the investment is given by $I = [I_0, I_1, \ldots, I_{n}]$, the present value is $I[0] + \sum_{i=1}^{n}\dfrac{I[i]}{(1+r)^i}$

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