# Problem 7
#
print( (1+0.07/365)^365 )


# Problem 8
#
S_n = 1000 # the initial amount S_0
n = 0
while( n<36 ){
    n = n+1
    S_n = (1+0.08/12) * S_n + 25
}
print(S_n)


# Problem 9
#
rho = 1+0.1/12
S_0 = 8000
numer = S_0 * rho^36
denom = (1 - rho^36)/(1-rho)
print( numer/denom )


# Problem 10
#
rs = c( 0.09, 0.1, 0.12 )
rho = 1+rs/12
S_0 = 100000
n_payoff = 30*12
numer = S_0 * rho^n_payoff
denom = (1 - rho^n_payoff)/(1-rho)
print( numer/denom )



# Problem 11
#
r = 0.09
rho = 1+r/12
S_0 = 100000
n_payoff = c( 30*12, 20*12 )
numer = S_0 * rho^n_payoff
denom = (1 - rho^n_payoff)/(1-rho)
bs = numer/denom
print('monthly payments=')
print(bs)

print('total amount payed=')
print(bs*n_payoff)


# Problem 12
#
rho = 1+0.1/12
b = 1000
n = 240
numer = ( b / (1-rho) ) * ( 1 - rho^n )
denom = rho^n
print(numer/denom)


# Problem 13
#
rs = seq( 0.09, 0.11, length.out=100 )
rhos = 1+rs/12
n = 240
S0 = 95000
lhs = (1-rhos) * rhos^n * S0 - 900 * (1-rhos^n)
plot( rs, lhs, type='l', xlab='yearly interest rate (r)' )
grid()
argmin = which.min(abs(lhs))
print(rs[argmin])