> 
> 30+31+31; 30+31+31+29+31+30; (30+31+31)/(30+31+31+29+31+30.0);

                                  92


                                 182


                             .5054945055

> S:=103.05+3*0.51; tmenot0:= 90/360.0;

                             S := 104.58


                        tmenot0 := .2500000000

> f:= i-> -S+ (1+i)^(0.5)* (3*(1-(1+i)^(-9))/i +100*(1+i)^(-9));

                                  /         1               \
                                  |  1 - --------           |
                                  |             9           |
                               .5 |      (1 + i)      100   |
         f := i -> -S + (1 + i)   |3 ------------ + --------|
                                  |       i                9|
                                  \                 (1 + i) /

> plot(f(i), i=-1..4, y=-S..200);plot(f(i), i=0..0.03, y=-S..50);


> g:= i-> -S+ (1+i)^(0.5)*
> (3*(1+i)^(-1)+3*(1+i)^(-2)+3*(1+i)^(-3)+3*(1+i)^(-4)+
> 3*(1+i)^(-5)+3*(1+i)^(-6)+3*(1+i)^(-7)+3*(1+i)^(-8)+103*(1+i)^(-9));

                        .5 /    1        3          3          3
  g := i -> -S + (1 + i)   |3 ----- + -------- + -------- + --------
                           |  1 + i          2          3          4
                           \          (1 + i)    (1 + i)    (1 + i)

              3          3          3          3         103   \
         + -------- + -------- + -------- + -------- + --------|
                  5          6          7          8          9|
           (1 + i)    (1 + i)    (1 + i)    (1 + i)    (1 + i) /

> -S+27+100; D(f);

                                22.42


                   1
            1 - --------
                       9
                (1 + i)      100
          3 ------------ + --------
                 i                9
                           (1 + i)
  i -> .5 -------------------------
                         .5
                  (1 + i)

                     /                   /       1    \            \
                     |                 3 |1 - --------|            |
                     |                   |           9|            |
                  .5 |        1          \    (1 + i) /      900   |
         + (1 + i)   |27 ----------- - ---------------- - ---------|
                     |          10             2                 10|
                     \   (1 + i)   i          i           (1 + i)  /

# non si semplifica
> fp:=
> i->.5/(1+i)^.5*(3*(1-1/((1+i)^9))/i+100/(1+i)^9)+(1+i)^.5*(27*1/((1+i)
> ^10*i)-3*(1-1/((1+i)^9))/i^2-900/(1+i)^10);

                         1
                  1 - --------
                             9
                      (1 + i)      100
                3 ------------ + --------
                       i                9
                                 (1 + i)
  fp := i -> .5 -------------------------
                               .5
                        (1 + i)

                     /                   /       1    \            \
                     |                 3 |1 - --------|            |
                     |                   |           9|            |
                  .5 |        1          \    (1 + i) /      900   |
         + (1 + i)   |27 ----------- - ---------------- - ---------|
                     |          10             2                 10|
                     \   (1 + i)   i          i           (1 + i)  /

> 
> i0:=0.03; f(i0); fp(i0); f(i0)/fp(i0);

                              i0 := .03


                              -3.0910843


                             -740.9372881


                            .004171856849

> i1:= i0-f(i0)/fp(i0);

                          i1 := .02582814315

> i2:= i1-f(i1)/fp(i1); 

                          i2 := .02590364117

> (i2+1)^2-1;

                              .052478281

>