%% seemst to be missing material 

%% example 4.3.1
iRate = .04
n=10
x=30
v = 1/(1+iRate)

iltable
A=0
A(40) = 0
format long
for k = 9:-1:0
    k
    Aold = A(30+k+1)
    Anew = v*q(30+k) + v*(1-q(30+k))*Aold
    A(30+k) = Anew;
end
disp(['val for insurance ' num2str(A(30))])
%% example 4.4.1

iltable

i = .06;
v = 1/(1+i);

delta = log(1+i);
ratio = i/delta;

% using exact expression (sum)

A1_35_30 = 0;

cohort = l(35);

for k=0:(30-1)
    term = v^(k+1)*(l(35+k)/cohort)*q(35+k);
    tt(k+1) = term;
    A1_35_30 = A1_35_30 + term;
end

disp('actuarial present value 30-year term life insurance')
A1_35_30

%% recursion

A=0
A(65) = 0
format long
xVal = 35
for k = 29:-1:0
 
    Aold = A(xVal+k+1);
    Anew = v*q(xVal+k) + v*(1-q(xVal+k))*Aold;
    A(xVal+k) = Anew;
end
Arecursion = Anew
A1_35_30-Arecursion

nPx = l(65)/l(35);

ApureEndowment = v^30*nPx

ActPresVal = ratio*Arecursion + ApureEndowment

%% example 4.4.2
iRate = .06

x=50
v = 1/(1+iRate)

iltable

DA = 0

format long
for k = 0:4
    kp50 = l(50+k)/l(50)
    q50pk = q(50+k)
    thisTerm = (5-k)*v^(k+1)*kp50*q50pk
    DA = DA + thisTerm
end
delta = log(1+i)
ratio = i/delta

DA = DA*ratio

disp(['val for insurance ' num2str(DA)])

%% problem 4.14
iRate = .05
n = 25

v = 1/(1+iRate)

% v = 1-iRate

a=v/60
APV1 = a*(1-v^n)/(1-v)

% second approach, from prob 4.6

a25 = (1-v^25)/iRate

APV1a = (1/60)*a25
   
% endowment part
APVendow = (v^25)*35/60

APV = APV1a+APVendow
APV = APV1+APVendow

%% 4.18

iRate = .06
v = 1+iRate

q(40) = 2.7812;
q(39) = 2.5982;
q(38) = 2.4313;
q(37) = 2.2791;
q(36) = 2.1042;
q(35) = 2.0136;
q(34) = 1.8980;
q(33) = 1.7927;
q(32) = 1.6965;
q(31) = 1.6089;
q(30) = 1.5289;

E0 = 10248.35
E1 = v*E0 - 100000*(q(30)/1000)
E2 = v*E1 - 100000*(q(31)/1000)
E3 = v*E2 - 100000*(q(32)/1000)
E4 = v*E3 - 100000*(q(33)/1000)
E5 = v*E4 - 100000*(q(34)/1000)