F = 100
lam = 0.10
m= 1 ## one coupon payments a year
C = 0.08 * F ## the coupon payment
n = 10*m ## how many payments do we make

## The price:
##
one_plus_lam = 1 + lam/m
P = F / one_plus_lam^n + (C/lam) * ( 1 - 1 / one_plus_lam^n )
print(P)

## The duration:
##
y = lam/m
c = C/F

pt_1 = (1+y)/(m*y)
numer = 1 + y + n*(c-y)
denom = m*c*((1+y)^n - 1) + m*y
pt_2 = - numer / denom
D = pt_1 + pt_2
print(D)