Mth302 solution

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 House Rent = 45 %= 0.45*2000 = 900
Utilities Allowance 200 Utilities allowance = 2.5 %= 0.025*2000=50
Medical/Group insurance 155 insurance/medical=5% = 0.05*2000 = 100
Miscellaneous Social Charges 186 Misc. Social Charges=5.8% =0.058*2000=116


Question 2:
The price of oil decreased from $76 per barrel to $70 per barrel. What is the percentage change in oil prices?
Solution:
Change = Final value – initial value
// = 76 – 70
//= 6
Percentage change = (Change / initial value) x 100%
Initial value =76$
Final value = 70$
Change = 6
% Change = (6/76) x 100 = 7.8947%
Marks 5

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:
S = Money accrued after n years also called compound amount = ?
P = Principal= 800
r = Rate of interest= 8% = 0.08
n = Number of periods = 3*2= 6 years (Semi annually)
S = P(1 + r/2)^ n
Compound interest = S - P
S= P(1+0.08/2)^3*2
S= 800(1+0.04)^6
S=1012.255 Rs
Compound interest = S - P
Compound interest = 1012.255 – 800 = 212.255 Rs
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.

Solution:

Accumulated value of n period = payment per period × accumulation factor for n Periods
Accumulated value of n period = C × [(1+i)^n – 1]/i

C = Cash flow per period = 500
i = interest rate = 8% = 0.08
n = number of payments = 3

= C* [(1+i)^n – 1]/i
= 500* [(1+0.08)^3 – 1]/0.08
= 500* [(1.08)^3 – 1]/0.08
= 500* [1.259712 – 1]/0.08
= 500* [0.259712]/0.08
= 500* 3.2464
=1623.2

Accumulated value of n period = 500 × 3.2464
Accumulated value of n period = 1623.2


Marks 5