from math import*
#Howard Philip J Frye : version simple
c=0.05
n=2000
while c < 10**9:
    c=c*1.0275
    n=n+1
print("en l'an :",n, "sans arrondir")






#Howard Philip J Frye : version rigoureuse
c=0.05
n=2000
while c < 10**9:
    c=c*1.0275
    c=(floor(c*100)+1)/100
    n=n+1
print("en l'an :",n)


#Deux frères
n=0
Ki=10**4
Hi=10**4
while Ki<=Hi:
    Ki=Ki*1.03
    Hi=Hi+400
    n=n+1
print("Ki a dépassé Hi au bout de ",n,"années")


#Harmonique
n=1
S=0
while S<10:
    S=S+1/n
    n=n+1
print("indice n=",n)
#bonus
n=1
S=0
for n in range(1,100):
    S=S+1/n
    print(S)
#Futurama
#question a)
M0=0.6
M=0
for n in range(9):
    M=M+2**n*(M0/(2**n*(n+1)))
print("valeur de Frye",M)

#question c)
def futura(M0,n):
    S=0
    for k in range(1,n+2):
        H=H+1/k
    return(M0*H)
#question d)
# Attention !ceci peut être trrrrrèèèèèès long...
n=1
S=0
while 0.6*S<100:
    S=S+1/n
    n=n+1
print("indice n=",n)