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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