Tuesday, May 11, 2010

MTH302 Business Mathematics & Statistics Solution 11, May 2010

9:14 AM | Posted by Xpert |
Question 1:

Basic Salary of John is 2000$ per month. According to his job contract
his allowances are some percentage of basic salary whereas other
benefits are percentage of Gross Salary. Details of his benefits are
as follows. What percent of Basic/Gross salary are these benefits?
(Show the calculations).
Marks 10

BENEFITS        $       Percent of Basic/Gross Salary
House Rent      900     45% (Basic Salary) / 29.03% (Gross Salary)
Utilities Allowance     200     10% (Basic Salary) / 6.45% (Gross Salary)
Medical/Group insurance 155     7.75% (Basic Salary) / 5% (Gross Salary)
Miscellaneous Social Charges    186     9.3% (Basic Salary) / 6% (Gross Salary)


PROPOSED SOLUTION:

Gross Salary:  = Basic Salary + House Rent + Utilities Allowance

Gross Salary: = $ 2000 + $ 900 + $ 200
Gross Salary will be $ 3,100

House Rent Percentage against Basic Salary: = (900 / 2000) * 100 = 45%
House Rent Percentage against Gross Salary: = (900 / 3100) * 100 = 29.03%

Utilities Allowance Percentage Against Basic Salary: = (200 / 2000) * 100 = 10%
Utilities Allowance Percentage Against Gross Salary: = (200 / 3100) *
100 = 6.45%

Medical / Group Insurance Percentage Against Basic Salary: = (155 /
2000) * 100 = 7.75%
Medical / Group Insurance Percentage Against Gross Salary: = (155 /
3100) * 100 = 5%

Miscellaneous Social Charges Percentage Against Basic Salary: = (186 /
2000) * 100 = 9.3%
Miscellaneous Social Charges Percentages Against Gross Salary: = (186
/ 3100) * 100 = 6%


Question 2:
The price of oil decreased from $76 per barrel to $70 per barrel. What
is the percentage change in oil prices?

SOLUTION:

Let us denominate the above values in Cells as follows:
Initial Oil Price: = $ 76
Final Oil Price: = $ 70
Change in Price: - $ 6
Percentage Change in Price: = (-6/ 76) * 100
Percentage Change in Price is  -7.89% which means the Oil prices
decreased by 7.89%



Question 3:
Suppose you took loan from a bank of amount 800£ at 8% interest
compounded semi-annually for three years. Find the compound interest.

SOLUTION:
Compounded Amount (S) = Principal (P) * (1+ interest rate (r) /100) ^
Number of Periods (n)
Principal: = 800
Interest Rate: =8%
Number of Periods: = 3*2 = 6 (semi annually)
Compounded Amount:
=800*(1+ (8/100/2)^6
=1012.255
Compound Interest:
=1012.255 – 800
=212.255 Pounds
Marks 5
 
 
Question 4:
Calculate the Accumulated Value if you deposit 500Rs at the end of
each year for the next 3 years?  Assume an interest of 8% compounded
annually.
Marks 5

SOLUTION:

Accumulated Value (S) = Annuity (r) * ((1+ Interest Rate (i) )^ Number
of years (n) – 1) / Interest Rate (i)
Accumulated Value (S) = Annuity or deposits  * Accumulation Factor for
‘n’ periods.

Annuity: =500
Interest Rate: = 8%
Number of Years: 3

Accumulated Value (A4): =500*((1+8%)^3)-1)/8%
Accumulated Value is 1623.2 Rs
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