CHAP 6 9 Business Mathematics

8/4/2019 CHAP 6 9 Business Mathematics

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Chapter 6

PAYROLL

DISTRIBUTION


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Chapter 6: PAYROLL DISTRIBUTION

Compensation income of the employees.

Compensation in remuneration for services performed by an employee.

Salaries, wages, bonuses, allowances, etc.

Payroll is a sheet of information containing the total wages of employees

for a specific period.

Types of compensation:

1. Salary

2. Time wage

3. Piece rate compensation

4. commission


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Salary

1. Weekly salary = annual salary / 52

2. Bi-weekly salary = annual salary / 26

3. Monthly salary = annual salary / 12

4. Semi-monthly salary = annual salary / 24

Time Wages- excess of regular hrs (overtime hrs)1. 1.3 x reg. hourly rate

2. 2.0 x reg. hourly rate


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To compute time wages :

Gross Pay = Reg. pay + overtime pay

Reg. Pay = No. of Hrs. worked x hourly rate

overtime Pay = No. of overtime hrs worked x overtime rate

Piece-Rate Compensation

The workers are paid for the no. of items produced or completed.

Types of Piece-Rate Compensation Plan

1. Straight piece-rate compensation plan

Ex: a cutter in a factory is paid P25 for every baby dress she cuts.In a day, she is able to cut 60 dresses. How much is her grosspay on that day?


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Soln

Gross Pay = Amt. per pc. Produced x No. of pcs. Produced

= P25.00 x 60

= P1,500.00

2. Piece-rate bonus compensation plan

Ex: An embroiderer is paid P13.00 for each cap embroidered for the1st 80 pcs. & P15.00 for each in excess of 80 pcs embroidered for 1week. If she embroidered 100 pcs. in a week, how much is her grosspay?

Soln

P13.00 x 80 pcs. = P1,040.00

P15.00 x 20 pcs. = P 300.00_________

100 pcs. P 1,340.00

______


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3. Graduated Piece-Rate Compensation Plan

Usually the amount paid per item increases as the workers output

increases.

Ex: The wrapping employees of a candy factory are paid per week onthe ff. graduated pc-rate compensation plan:

P20 per hundred pcs. For the 1st 300 pcs. wrapped



Soln

1st 300 pcs wrapped 300/100 = 3 x P20 = P 60

2nd

400 pcs wrapped 400/100 = 4 x P25 = P100In excess of 700 pcs 2,420/100 = 24.2 x P30 = P726

3,120 pcs. P886

________ ____


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Commissions

Commission = Amt. of sales or purchase made x commission rate

Commission Rate = Commission / amt. of sales or purchase made

Amt. of sales = Commission / Commission rate

1. Straight commission

2. Commission & Bonus

3. Commission Plus Override- earn commissions on all sales they make + a% on the other sales of their representatives.

4. Salary & Commission- person received basic salary + a % on the sales orcollections made


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Net Pay

Gross Pay/ Gross Income- Total earnings; amt. received by the employeew/o deductions.

Net Pay/ Net Income - Deductions are made from the gross pay

- subtract the sum of all the deductions from the gross pay

Ex: Mr. P gross pay for the month of June is P22,500. His deductions areSSS Premium, P83.30; withholding tax, P87.52; & Medicare P12.50. Findhis net pay.

Soln Gross Pay P 22,500.00

DeductionSSS Premium P83.30

Withholding Tax P87.52

Medicare P 12.50 P 183.32

Net Pay P 22, 316.68

__________


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Chapter 8

BORROWING &

LENDING MONEY


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Chapter 8: BORROWING & LENDING MONEY

Suppose the principal Pis invested at the rate rfor t years. Thus the

simple interest Iis computed based on the original principal duringthe whole time multiplied by the product of rate r & time t, that is

It follows that I= Prt t = IPr

__

r = IPt

__

Let F be the final amountresulting from the investment of P for t years atthe rate r, & I be the interest rate at the end of t years.

F = P + I

= P + Prt

= P (1+ rt)

* Note that the time unitwill be in terms of year, unless specified.


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Principal in Terms of Final Amount

Deduce from F = P (1+rt) the formula for P, i.e.

P = F

1+ rt____

Example: Mrs. Yen invested P20,000 w/c accumulates to P22,500in 10 months. Find the simple interest rate.

Solution:

P = P20,000, F= P22,500, t= 10 months or 5/6 year.

From the formula I=Prt, e have = I = F-P = 2,500rPt Pt 20,000 (5/6)

__ ___ __________ = 0.15 or 15 %


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Timet

If the time is expressed in months, then use t =___________No. of months

12

For the time to be in terms. To solve for t, we have 1+ rt = FP

___

Or rt = F

P

___ - 1

The tis given by the formula

t = ( )r1__ __

P

F - 1

Time Conversion

If the time is in terms of:

a) months, then divide by 12

b) Semiannual pds, the divide by 2

c) Quarterly pds, then divide by 4

d) Bimonthly pds, then divide by 6

e) Semimonthly pds, then divide by 24


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If the time is expressed in days, the there are 2 kinds of time to convert theno. of days in D in yrs.

a) t =__________ = __________ , for exact interest

b) t =__________= __________ , for ordinary interestNo. of days

No. of days

360 360

365 365

D

D

* Ordinary interest is usually applied in Bankers Rule.

Example: 0.25 year is equivalent to 0.25 x 12 = 3 months.

: Convert 2.6 yrs in terms of the no of months & semiannual pds.

To convert the no of yrs to semiannual pds, multiply by 12

2.6 x12 = 31.2 or 31 1/5 monthsTo convert the no of yrs to semiannual pds, multiply by 2

2.6 x 2 = 5.2 semiannual pds

Converting 1.15 yrs in months

1.15 x 12 = 13.8, 13 8/10, or 13 4/5 months


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2 Kinds of Interest Rates

Interest Rates

Since the no. of daysD is expressed in 2 ways, then there are 2 varieties ofinterest rates.

a) Exact Interest forD days,

I = Pr ______

365

De

b) Ordinary Interest forD days,

I = Pr ___oD

360


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o1

Io1 360

Time Between 2 dates

1. Actual Time - no. of days is obtained by counting all the days, inclusivebetwn 2 given dates including the last day but not the 1st day.

2. Approximate Time - assumes that every months counts 30 days

Interest Rate Betwn 2 Dates

4 Varieties :

1. Ordinary Interest at actual no. of days = Io1

= Prt = Pr ( Actual time )

2. Ordinary Interest at approximate no. of days =Io2

Prto2

Io2

= = Pr ( Approximate time )

360


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3. Exact Interest at actual no of days =I

e1

e1

I = Prt = Pr ( Actual time )

365e1

4. Exact Interest at approx. no. of days = e2

I

= Prt = Pr (Approximate time )e2

e2

I

365


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Chapter 9

SIMPLE DISCOUNTS


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Chapter 9 : SIMPLE DISCOUNTS

Principal & Discount

Discounts on amt. F.

To find the present valueP ofFmeans to discountFfor tyears.

The discountdenoted byIon the amtFis defined as the difference between thefuture valueF& its resent valueP, that is

I= F - P

I = interest on the present valueP

; discount on the amtF

.The symbolIhas 2 useful names.

I =Interest onP

Discount onF


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Simple Discount

The discount D on a given amt F at a discount rate d due at the end of tyears is given by

D = Fdt

The present value ofP of F is

P = F D

= F - Fdt

P = F (1-dt)


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Promissory notes

-Is a written promise done by a borrower to pay certain sum to the lender within aspecified time.

-Proceeds sum or amount the borrower receives.

Features of Promissory Notes

1. Date of the note date when the note is done

2. Maturity date date when the note is due

3. Term of the note length of time from the date of the note to the maturitydate

4. Face Value principal amount stated on the note

5. Maturity Value principal plus interest


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Relations Betwn Interest rate ( r ) & Discount Rate ( D )

D = Fdt, then P= F - D

= F Fdt

= F ( 1- dt )

Since P = F , then it follows that

1+rt F = F (1-dt )1+rt

1+rt1 = 1 - dt

Solving for d, we get

d = r1+rt

Solving for r gives

r = d .1- dt

CHAP 6 9 Business Mathematics

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