15: Compound Interest

Example number 15.1, Page number 15.4

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
P=4000;    #principal(Rs)
R=5;       #rate(%)
T=2;       #time(yrs)
n=1;

#Calculation
A=P*(1+(R/(100*n)))**(n*T);     #amount(Rs)

#Result
print "amount is",A,"Rs"

amount is 4410.0 Rs

Example number 15.2, Page number 15.4

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
P=2000;    #principal(Rs)
R=10;       #rate(%)
T=3;       #time(yrs)

#Calculation
x=R/100;
y=(1+x)**T;
CI=P*(y-1);        #compound interest(Rs)

#Result
print "compound interest is",CI,"Rs"

compound interest is 662.0 Rs

Example number 15.3, Page number 15.5

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
R=10;       #rate(%)
T=2;       #time(yrs)
A=968;     #amount(Rs)

#Calculation
P=A/(1+(R/100))**T;     #principal(Rs)

#Result
print "principal is",P,"Rs"

principal is 800.0 Rs

Example number 15.4, Page number 15.5

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
P=64000;    #principal(Rs)
R=2.5;       #rate(%)
T=3;       #time(yrs)

#Calculation
x=R/100;
y=(1+x)**T;
CI=P*(y-1);        #compound interest(Rs)

#Result
print "compound interest is",CI,"Rs"

compound interest is 4921.0 Rs

Example number 15.5, Page number 15.5

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
P=2000;    #principal(Rs)
R=8;       #rate(%)
T=9/12;       #time(yrs)
n1=4;
n2=2;
n3=1;

#Calculation
A1=P*(1+(R/(100*n1)))**(n1*T);   #amount(Rs)
CI1=A1-P;     #compound interest in 1st case(Rs)
A2=P*(1+(R/(100*n2)))**(n2*T);   #amount(Rs)
CI2=A2-P;     #compound interest in 2nd case(Rs)
A3=P*(1+(R/(100*n3)))**(n3*T);   #amount(Rs)
CI3=A3-P;     #compound interest in 3rd case(Rs)

#Result
print "compound interest in 1st case is",int(CI1),"Rs"
print "compound interest in 2nd case is",round(CI2,1),"Rs"
print "answer given in the book is wrong"
print "compound interest in 3rd case is",round(CI3),"Rs"
print "answer varies due to rounding off errors"

compound interest in 1st case is 122 Rs
compound interest in 2nd case is 121.2 Rs
answer given in the book is wrong
compound interest in 3rd case is 119.0 Rs
answer varies due to rounding off errors

Example number 15.6, Page number 15.6

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
R=4;       #rate(%)
T=2;       #time(yrs)
CI_SI=50;    #difference between CI and SI(Rs)

#Calculation
x=(R/100)**2;
P=CI_SI/x;     #sum(Rs)

#Result
print "sum is",P,"Rs"

sum is 31250.0 Rs

Example number 15.7, Page number 15.6

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
R=10;       #rate(%)
T=2;       #time(yrs)
P=2000;     #sum(Rs)

#Calculation
x=(R/100)**2;
CI_SI=P*x;     #difference between CI and SI(Rs)

#Result
print "difference between CI and SI is",CI_SI,"Rs"

difference between CI and SI is 20.0 Rs

Example number 15.8, Page number 15.7

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
CI=282.15;      #compound interest(Rs)
SI=270;      #simple interest(Rs)
T=2;     #time(yrs)

#Calculation
R=(CI-SI)*100*T/SI;    #rate per annum(%)
P=100*SI/(R*T);     #sum(Rs)

#Result
print "rate per annum is",R,"%"
print "sum is",P,"Rs"
print "answer given in the book is wrong"

rate per annum is 9.0 %
sum is 1500.0 Rs
answer given in the book is wrong

Example number 15.9, Page number 15.7

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
R=10;       #rate(%)
T=3;       #time(yrs)
CI_SI=31/2;   #difference between CI and SI(Rs)

#Calculation
x=R/100;
y=(x**3)+(T*(x**2));
P=CI_SI/y;     #sum(Rs)     

#Result
print "sum is",P,"Rs"

sum is 500.0 Rs

Example number 15.10, Page number 15.7

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=434;
b=272;

#Calculation
Nr=a-b;     #numerator of fraction
Dr=b;     #denominator of fraction
d=(Nr**2)-(4*Dr*Nr);       #discriminant
q=(-Nr-math.sqrt(abs(d)))/(2*Dr);    #solution
R=(-q-1)*100;         #rate(%)

#Result
print "rate percent is",round(R,3),"%"
print "answer given in the book is wrong"

rate percent is 0.977 %
answer given in the book is wrong

Example number 15.11, Page number 15.8

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
R=5;      #rate(%)
A=50440;    #debt amount(Rs)
T=3;    #time(yrs)

#Calculation
x=100/(100+R);
y=x*(1+x+(x**2));
a=A/y;     #annual payment(Rs)

#Result
print "annual payment is",a,"Rs"

annual payment is 18522.0 Rs

Example number 15.12, Page number 15.8

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
P=1;    #assume
A=1.44*P;    #amount(Rs)
T=2;    #time(yrs)
N=2;

#Calculation
R=(math.sqrt(A/P)-1)*100;      #rate(%)
T=(N-1)*100/R;     #time(yrs)

#Result
print "time is",T,"years"

time is 5.0 years

Example number 15.13, Page number 15.8

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
I2=238.50;    #interest in second year(Rs)
I1=225;       #interest in first year(Rs)
T=1;    #time(yrs)

#Calculation
I=I2-I1;     #interest on 1 year(Rs)
R=100*I/(I1*T);    #rate per annum(%)

#Result
print "rate per annum is",R,"%"

rate per annum is 6.0 %

Example number 15.14, Page number 15.9

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
CI_SI=20;     #difference for 2 years(Rs)
CISI=61;      #difference for 3 yrs(Rs)
T1=2;     #time(yrs)
T2=3;     #time(yrs)

#Calculation
R=((CISI/CI_SI)-T2)*100;    #rate(%)
P=CI_SI*(100/R)**2;     #sum(Rs)     

#Result
print "sum is",P,"Rs"

sum is 8000.0 Rs

Example number 15.15, Page number 15.9

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=3;    #time(yrs)
P=1000;    #sum(Rs)
A=1331;    #amount(Rs)

#Calculation
x=(A/P)**(1/T);
R=100*(x-1);      #rate per annum(%)

#Result
print "rate per annum is",R,"%"

rate per annum is 10.0 %

Example number 15.16, Page number 15.9

In [22]:
#importing modules
import math
from __future__ import division

#Variable declaration
P=64000;    #sum(Rs)
CI=4921;    #compound interest(Rs)
R=5;     #rate(%)
n=2;

#Calculation
A=P+CI;    #amount(Rs)
x=A/P;
y=(1+(R/(100*n)))**n;
T=math.log(x)/math.log(y);      #time(years)

#Result
print "time is",T,"years"

time is 1.5 years