# 10.11.jl
# 2024-10-12
# $Id: 10.11.jl 1.1 2024/11/03 07:04:33 s Exp $
#
# a : amount
# d : discount factor, d[k] = d(0,k)
# f : forward rate, f[k] = f(k-1,k) 
# g(r) : pv2 - pv1
# pv1 : present value in variable rate
# pv2 : present value in fixed rate
# r : fixed rate
# s : spot rate, s[k] = s(k)
# x : cash flow in variable rate, x[0] = x(k)
# y : cash flow in fixed rate, y = a * r

using Printf

function g(a,r,pv1) # g=pv2-pv1
    d1= 1 / (1 + r) ^ 1
    d2= 1 / (1 + r) ^ 2
    d3= 1 / (1 + r) ^ 3
    d4= 1 / (1 + r) ^ 4
    d5= 1 / (1 + r) ^ 5
    d6= 1 / (1 + r) ^ 6
    y = a * r
    y * (d1 + d2 + d3 + d4 + d5 + d6) - pv1
end

# input
s = [0.070, 0.073, 0.077, 0.081, 0.084, 0.088]
f = [0.0,   0.0,   0.0,   0.0,   0.0,   0.0]
a = 1000.0
n = length(s)

# calculation
for i = 1:n
    if i == 1
        f[1] = s[1]
    else
        f[i] = (1 + s[i]) ^ i / (1 + s[i - 1]) ^ (i - 1) - 1
    end
end

x   = a .* f
i   = 1:n
d   = 1 ./ (1 .+ s) .^ i
pv1 = sum(x .* d)

r = 0
for i = 8700: 8900
    global r = i / 1e5
    if g(a,r,pv1) > 0
        break
    end
end

# output
println("10.10.jl")
println("a ", a)
println("s ", round.(s, digits=3))
println("f ", round.(f, digits=3))
println("x ", round.(x, digits=3))
println("d ", round.(d, digits=3))
println("pv1 in variable rates ", pv1)
println("(r, g(r))= (", r,", ",  g(a,r,pv1),")")
# end