421.sagews

def units(C, n, F, r):
    return C * ((1 - (1 / (1 + r) ^ n)) / r) + F * (1 / (1 + r) ^ n)
    
def price(C, n, F, r):
    return 100 * (units(C, n, F, r) / F)

# price yield: from 0 to 10% yields
plot(price(70,4,1000,var('r')),0,.1)

# price yield over time: ranging from 1 to 5 periods and 1% to 10% yield
plot3d(price(70,var('n'),1000,var('r')), (n,1,5), (r,.01,.1))