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Assignment #  1

Solution 1:

Present Value (loan)                 P          =?
Interest rate/annum                   i           =7%
Interest rate/month                    i           =7/12%            =0.005833      

Amount                                    R          =8450 Rs
Number of years                       N         =17
Number of periods                   n          =17*12            = 204

Using Formula              P=R(1-(1+i)-n)/i

Putting Values                           P=8450(1-(1+0.005833)^-204)/0.005833
                                                P=8450(1-(1.005833)^-204)/0.005833
                                                P=8450(1-0.3053)/0.005833
                                                P=8450(0.6947/0.005833)
                                                P=8450*119.098
                                                P=1006380 Rs


Solution 2:

Basic Salary                 =30000 Rs
Allowances                   =18000 Rs
Taxable Income            =?

% allowances               = (18000/30000)*100
                                    =60%
Allowed non taxable allowance =50%
                                                            =0.5*30000
                                                            =15000 Rs

So taxable allowances                           =60%-50%
                                                            =18000-15000
                                                            =3000 Rs
Hence 3000 Rs of allowances are taxable

Total taxable income                             =30000-3000
                                                            =33000 Rs



Solution 3:

(a)

Absent students             =3
Total students                            =24
% of students absent                 =?

% of students absent     =3/24*100
                                    =12.5%

(b)

%age of students absent                        =12.5%
Total students                                        =24
How many students are absent               =?

How many students are absent               =12.5% of 24
                                                            =12.5/100*24
                                                            =3
(c)

12.5% of class                                      =3 students
Total students enrolled in the class         =?

                                                            12.5/100* Total students enrolled in the class=3
Total students enrolled in the class         =3*100/12.5
                                                            =24


Solution 4:

Principle                                   P          =?
Interest rate/annum                   r           =25%
Interest rate/month                    r           =25/12%          =0.02083        

Accumulated Amount               A         =100,000 Rs
Number of years                       N         =5
Number of periods                   n          =5*12  = 60
Compound interest                               =?
Using Formula
                                                     A=P(1+r)^n
                                         100000 =P(1+0.02083)^60
                                           100000 =P(1.02083)^60
                                                100000 =P(3.445)
                                                  P=100000/3.445
                                                    P=29027.6 Rs

Compound interest                    =100000-29027.6
Solution 5:

                                                     =70972.4 Rs



Total payment                           P          =150000 Rs
Withdrawal after each 3 month    R       =6000 Rs
Interest rate/annum                   i           =12%
Interest rate/quarterly                i           =12/4%            =0.03  

Number of withdrawal  n          =?
Using Formula 

                        P=R(1-(1+i)^-n)/i
Putting Values

                        150000=6000(1-(1+0.03)^-n/0.03
                        150000=6000(1-(1.03)^-n/0.03
                        150000*0.03/6000=1-(1.03)^-n
0.75=1-(1.03)^-n
(1.03)^-n=1-0.75
(1.03)^-n=0.25

Taking Log
Log(1.03)^-n=log0.25
-n log 1.03= -0.60205999
n(0.01283722)= 0.60205999

As

n = 0.60205999/0.01283722
n = 46.899
Number of withdrawal           n  = 47