Mathematics for Business
Question 1
Complete the table below (Show your work)
-
M T W Th F Sa
Total Hours
Regular Hours
Overtime Hours
Regular Rate
Overtime Rate
10hr 10hr 10hr 9hr 9hr 6 hr
54
40
14
$ 7.50
$11.25
Workings:
Total hours worked in a week = 10 + 10+ 10 + 9 + 9 + 6 = 54 hrs
regular hours = 54 hrs – 40 hrs = 14 hrs
overtime rate = overtime as a decimal * regular rate
= 1.50 * $ 7.50
= $11.25
b)
Gross earning of the employee = amount of money employee earned for time worked
for regular hours = 40hrs * $7.50 = $ 300
for overtime hours = 14 hrs * $11.25 = 157.5
Total gross pay = $ 300 + 157.5 = $ 457.5
1. (B) Hamad Gross pay
salary for the for weeks = $ 750 * 4 weeks = $ 3000
commission = 55,000 * 7% = $3850
Total gross pay = $6850
1. (C) Jasem Gross pay
He produced over 200 units which is charged at $7.25
Thus: 230 units * $7.25 = $1 667.50
= $1 668
2. (A) (a)
Finding the number of days of the loan from March 15 until June 11
number of days = 88 days
b) interest amount =
I = PRT
= $60 000 * (5.35/100) * (88 days/ 365 days)
= $60 000 * 0.0525 * 0.24109589
= $ 759.45
I = $ 759
2. (B)
calculating balance due
finding total interest =
I = P rt
I = $5000 * 3/100 * 120/360
I = 5000 * 0.03 * 0.3333
I = $50
Total amount to be paid = $5000 + $50
Thus Ending balance due = $5050 – $2000 (amount already paid) = $3050
2. (C)
Finding the interest and maturity value
Interest = PRT
= $14000 * 0.07* 15/12
= 14 000* 0.07 * 1.25
= $1,225
maturity rate = P + I
= $14,000 + 1,225
= $15,225
3. (A)
Calculating what he will have in the account
finding interest
I = P [ (1+r) ^n – 1]
= $14,850 [ (1+04) ^5-1 (n= 3 yrs to pay*2-1 = 5)
= $ 14,850 [ (1.04)^5-1)
= $14,850 (1.217-1)
=$14,850 (0.217)
= $ 3,222.45
= $3,222
Amount in the bank after 3 years = P + I
= $14,850 + 3,222.45
= $18, 072
3 (B)
Finding the present value of $35,900
( i=8%/ 2 six-month periods= 4%) (n=10 years*2=20)
FV = PV *(1.00+i)^n
= $35,900 * (1.00+0.04)^20
= $35.900 * (1.04)^20
= $35,900* 2.191
= $ 78, 661
3. C.
Finding the effective rate (APY) = (1 + r/n)^n-1
= (1+0.12/4)^4-1
= 0.126 (*100)
= 12.55 %
=13%
4 . A)
PM = FV * r / ((1+r)^N – 1) (10%/2 = 0.05% and N =7 years * 2 = 14)
= $18,000 * 0.05 / ((1+0.05)^14-1)
APR = $918.43
4 B)
FV = PM ((1+r) ^N-1) /r
= $750 ((1+0.03)^36-1) /0.03
= 47,456.95
= $ 47,457
4) C
FV = PM ((1+r) ^N-1) /r
= 1,250 ((1+0.04) ^40-1)/0.04
= $118, 782 (amount to be invested today to get the annuity)
5. A.
Finding the monthly payment for the car
Amount of loan=Car price - down payments + charges
=19,000 – 1,400 + 4,900
=$ 22,500
amount to be paid for 20 months
= $22,500/ 20 months
= $1.125 per month
5. B
Calculating APR
amount to remaining $ 9,000 – 3,800 = $5,200
finding the amount on interest to be paid I = PRT
= 5,200 * (288.50/5,200) * 1.67
= $481.795
finding APR = 24*I
P (T+1)
= 24($481.795)
5200*(1+20)
= 0.1058 (which is in the table)
5. C
calculating the monthly payment
amount of loan $ 190,000 – $40,000 = $150,000
Interest rate = PRT
finding the monthly payment $ 150,000 * 30,000/ 190,000 * 120/12
= $236.835
= $236.84