Blog: MTH302 Assignment No. 1 Fall 2011 solution

Assignment # 1

MTH302 (Fall 2011)

Total marks: 30

Lecture # 1 to 8

Due date: 01-11-11

Question No. 1:

A company bought shares at Rs. per share and sold them after year at Rs. With a commission rate of buying and selling the stock. What is its return on investment?

Question No. 2:

In a domestic business an owner invests 15,000 Rs at 15% per annum for a period of 66 months. Calculate compound interest and also future value.

Question No. 3:

How much money deposited now will provide payments of Rs. 10,000 at the end of each quarter for 15 years if interest is 12% compounded quarterly.

Solution:

Question No. 1:

A company bought shares at Rs. per share and sold them after year at Rs. . With a commission rate of buying and selling the stock. What is its return on investment?

Answer:

shares at Rs.56.27 = 56270

Commission at 1.2% = 56270*1.2/100 = 675.24

Total cost = 56270+ 675.24

= 56945.24

Sold:

1000 shares at Rs. = 65250

Commission at 1.2% = 65250*1.2/100

= 783

Total Sale = 65250- 783 = 64467

Gain

Net receipts = 64467

Total cost = 56945.24

Net Gain = 64467 - 56945.24 = 7521.76

Return on investment = 7521.76/56945.24*100

= 13.20%


Complete solution:



Question No. 1:
A company bought shares at Rs. per share and sold them after year at Rs. . With a commission rate of buying and selling the stock. What is its return on investment?


Solution


shares at Rs.56.27 = 56270
Commission at 1.2% = 56270*1.2/100 = 675.24
Total cost = 56270+ 675.24
= 56945.24
Sold:
1000 shares at Rs. = 65250
Commission at 1.2% = 65250*1.2/100
= 783
Total Sale = 65250- 783 = 64467
Gain
Net receipts = 64467
Total cost = 56945.24
Net Gain = 64467 – 56945.24 = 7521.76
Return on investment = 7521.76/56945.24*100
= 13.20%




Question No. 2:
In a domestic business an owner invests 15,000 Rs at 15% per annum for a period of 66 months. Calculate compound interest and also future value.
For details lec no6 page 58


Solution
S = Money accrued after n years also called compound amount
P = Principal = 15000
r = Rate of interest = 15%
n = Number of periods 66months / 12 =5.5years
S = P(1 + r/100)^ n
Compound interest = S – P
So…


S (this is future value also)= 15000(1+15/100)^5.5
Future value = 32354.105
copound intrest=S-P
= 32354.105-15000
= 17354.105
we can also find fv by this formula ans will be same
fv (future value)= pv(present value)*(1+i)^n




Question No. 3:
How much money deposited now will provide payments of Rs. 10,000 at the end of each quarter for 15 years if interest is 12% compounded quarterly.
Foe details lec no7 page 62
Solution


in our question…
C = Cash flow per period = 10000 at the end of each quarter
i = interest rate 12% compounded quarterly 12/100 = 0.12
n = number of payments. 15years*4= 60 because intrest compounded quarterly 


so…


pv = 10000*[1-(1+0.12)^-60/0.12]
= 10000*[1-(1.12)^-60/0.12]
= 10000*[0.9907]
= 9907.16