mth302 assignment 1 solution

Question 1:
If you want to get a loan with interest rate 7% per annum compounded monthly for a
period of 17 years and pay Rs. 8,450 at the end of per month for this loan, then how much
will you borrow?
We have to find
Loan payment P=?
R=monthly installment=Rs.8, 450
N=17*12=204 204
7
7% . % . 0.00583333
12
1 (1 )
1 (1 0.005833)
8450
0.005833
1 (1.005833)
8450
0.005833
1
1
(1.005833)
8450
0.005833
1
1
3.275
8450
0.005833
1
8450
n
n
n
i p a p m
AS
i
P R
i
so
P
P
P
P
P
-
-
-
= = =
- + é ù
=
ê ú
ë û
- + é ù
=
ê ú
ë û
- é ù
=
ê ú
ë û
é ù
-
ê ú
=
ë û
é ù
-
ê ú
=
ë û
=
0.305
0.005833
8450 119.090
1006317.0458
p
p
- é ù
ê ú
ë û
´ =
=
P= Rs.1006317.0458
Question 2:
If the basic salary of an employee is Rs. 30000 and allowances are Rs. 18,000.
What is the taxable income of the employee?
Solution:
See also example on page no.24 on handouts.
The salary of an employee is as follows:
Basic salary = Rs.30, 000
Allowances=RS.18, 000 WHAT IS THE TAXABLE INCOME OF THE COMPANY=??
% allowance =
18,000
100 60%
30,000
æ ö
= ´
ç ÷
è ø
Allowance non taxable= 50%
   = ´ = 0.5 30,000 .15,000 Rs
Taxable allowance =60%-50%
   =18,000-15,000=Rs.3000
Hence 3000 Rs. Of allowances are taxable
Total taxable income=30,000+3,000=Rs.33, 000
Question 3:
(a) If 3 students are absent out of a class of 24, what percent of the students are absent?
(b) If 12.5% of the students are absent in a class of 24, how many students are absent?
(c) If 3 students are absent and these comprise 12.5% of the class, how many students are
enrolled in the class?
Solution:
(a).
  Absent students=3
  Total students =24
% of students absent
3
100
24
12.5%
æ ö
= ´ ç ÷
è ø
=
    =12.5%
(b).
  %age of students absent=12.5%
  Total students=24
How many students are absent=12.5% of 24
    
12.5
24
100
3students
æ ö
= ´ ç ÷
è ø
=
     = 3 students
(c).  
    12.5% of class=3 students    
12.5
3
100
100
3
12.5
24
class students
class
class students
æ ö
ç ÷´ =
è ø
æ ö
= ´ç ÷
è ø
=
    Over all class will be =24 students
Question 4:
What principal does Ali need to invest at 25% p.a.(per annum) compounding
monthly so that he ends up with Rs. 100,000 at the end of five years? Also
find compound interest.
Solution:
consider the formula for computing compound
interest:
1
nt
r
A P
n
æ ö
= + ç ÷
è ø
The letters in this formula are
A for the total amount of money accumulated
P for the principal or initial money deposited
r for the interest rate as a decimal
n for the number of times each year the interest is compounded
t for the number of years involved
here in question
100,000.
25% .
12
5
A Rs
r p a
n
t
=
=
=
=
By putting the values in formula ( )
12 5
12 5
60
0.25
100,000 1
12
100,000 1 0.0208333
100,000 (1.0208333)
100,000 (3.4458039)
100,000
3.445803
29020.8
P
P
P
P
P
P
´
´
æ ö
= + ç ÷
è ø
+ =
=
=
=
=
SO PRINCIPAL AMOUNT WILL BE= Rs.29020.8
Compound interest= 100,000-29020.8
Compound interest = Rs.70979.2
Question 5:
A retired person wants to deposit his G.P. fund savings of Rs. 1,50,000 in a bank. The
bank offers 12% interest compounded quarterly, so as to withdraw Rs. 6000 after each
three months. Find the number of withdraws.
[ (1.03) 0.25
-n
= Shows n = 47]
Solution:
Payment = P =Rs.150, 000
Withdrawal =R=Rs.6000 after each three months
12
% 3% 0.03
4
i = = =
TO find n As
1 (1 )
1 (1 0.03)
150,000 6000
0.03
1 (1.03)
150,000 6000
0.03
150,000 0.03
1 (1.03)
0.03
0.75 1 (1.03)
(1.03) 1 0.75
(1.03) 0.25
,log
log(1.03) log(0.25)
log1.03 0
n
n
n
n
n
n
n
n
i
P R
i
so
taking
n
-
-
-
-
-
-
-
-
- + é ù
= ê ú
ë û
- + é ù
=
ê ú
ë û
- é ù
=
ê ú
ë û
´
- =
- =
- =
=
=
- = - .60205999
(0.012837224) 0.60205999
0.60205999
0.01283722
46.899
47
n
n
n
n
=
=
=
=
 No. of withdrawal =N=47
If you do not want to take log then according to statement of teacher as in assignment
(1.03)
-n
=0.25 shows n=47