maths

Mathematics for Business

Question 1

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