P = 100
n = 10
rates = [0, .02, .05, .1]

PV = []
for r in rates:
    PV.append([P / (1 + r) ** t for t in range(1, n+1)])
    print("r={}".format(r))
    print("Payment Values:")
    print(PV[-1])
    print()

plt.rcParams["figure.figsize"] = [8,6]

#And now, let's graph them
for payments, r in zip(PV, rates):
    #Use "o" so we get points instead of a line
    plt.plot(list(range(1,n+1)), payments, "o", label="r="+str(r))

    #Set the limits so that we have 0 as the left minimum and 5.5 as the right (so we don't cut off points)
    plt.xlim([0,10.5])
    plt.ylim([0,110])
plt.xlabel("t")
plt.ylabel("Payment PV")
plt.title("Present Value of Annuity Payments")
plt.legend()
plt.show()

#Iterate through and find the present values
for r, payments in zip(rates, PV):
    print("r={}".format(r))
    print("Payment Values: {}".format(sum(payments)))
    print()

for r, payments in zip(rates, PV):
    print("r={}".format(r))
    #If r is 0 then there will be division by 0
    #Formula is n*payment in that case
    if r > 0:
        print("Payment Values: {}".format(annuity_TVM(100,10,r)))
    else:
        print("Payment Values: {}".format(10 * 100))
    print()