#ejemplo 03.01
n,i=var("n,i")
s(n,i)=((1+i)**n-1)/i
a(n,i)=s(n,i)/(1+i)**n
R=9192
T=7
r=0.0805
N=2
i1=r/N; print i1
n1=N*T; print n1
print s(n1,i1)
print a(n1,i1)
A=R*a(n1,i1); print A
S=R*s(n1,i1); print S

0.0402500000000000
14
18.3233122859768
10.5457104013097
96936.1700088392
168427.886532699

#ejemplo 0302
r=.6807
N=12
T=10

n,i=var("n,i")
s(n,i)=((1+i)**n-1)/i
show(s(n,i))

$$\newcommand{\Bold}[1]{\mathbf{#1}}\frac{{\left(i + 1\right)}^{n} - 1}{i}$$

i1=r/N; print i1
n1=N*T; print n1
print s(n1,i1)
S=731670
R=S/s(n1,i1); print R

0.0567250000000000
120
13215.5244454120
55.3644316593134

#ejemplo 0303
A=60719.22
r=.5902
N=4
T=7

n,i=var("n,i")
a(n,i)=s(n,i)/(1+i)**n
show(a(n,i))

$$\newcommand{\Bold}[1]{\mathbf{#1}}\frac{{\left(i + 1\right)}^{n} - 1}{{\left(i + 1\right)}^{n} i}$$

i3=r/N; print i3
n3=N*T; print n3

0.147550000000000
28

print a(n3,i3)

6.63366402461113

R=A/a(n3,i3); print R

9153.19494245254

#ejemplo 03.04
"""
Una persona obtiene un préstamos de $41654.76, acordando pagar capital 
e intereses al 23.67% convertible semestralmente mediante pagos de 
$13666.552677683812 cada uno, haciendo el primero al final del primer periodo. 
¿Cuantos pagos deberá hacer?
"""
A=41654.76
r=0.2367
N=2
R=13666.55
i=r/N; print i

0.118350000000000

n = (log(R)-log(R-A*i))/log(1+i); print n

4.00000098839900

R/(R-A*i)

1.56426747864703

log(R/(R-A*i))

0.447417649653330

#ejemplo 03.05
A=929.99*(1-0.31); print A

641.693100000000

R=32.49
N=12
n=60
###planteamiento
i=var("i")
eqn = ((1+i)**n)*(R-A*i)==R
show(eqn)

$$\newcommand{\Bold}[1]{\mathbf{#1}}{\left(i + 1\right)}^{60} {\left(-641.693100000000 \, i + 32.4900000000000\right)} = 32.4900000000000$$

eqn.roots(i, ring=RR, multiplicities=False)
#eqn.find_root(0,1)
#solve([eqn], i)

[-3.05113903876477,
 -1.59652742007444,
 -1.47272915885186,
 0.000000000000000,
 0.0475052406189654]

i=0.0475052406189654
r=N*i; print r

0.570062887427585

T=n/N
r_ef=((1+i)**n-1)/T; print r_ef

3.03893520162589