EARNING MONEY

When people are employed to carry out a task they are paid a wage or salary.
The person or organisation that employs them is called the employer and the person who is employed is called the employee.

A wage is an hourly rate of pay for a standard number of hours and is usually paid weekly. When wage earners work more than the standard number of hours the extra hours are called "overtime" and are usually paid at a higher rate.
The two most common rates of pay for overtime are:
time-and-a-half: this is the standard hourly rate of pay multiplied by 1½
double-time: this is the standard hourly rate of pay multiplied by 2.

A salary is an annual rate of pay which is normally paid to the employee in weekly, fortnightly or monthly installments. Salary earners are not normally paid extra if they work extra hours i.e. they don't earn overtime.

Example 1:
David is paid $18.00 per hour for a 38 hour week. If he works 46 hours in a week with overtime being paid at time-and-a-half, how much does he earn for the week?

Normal time = 38 x $18.00 = $684.00
Extra hours = 46 - 38 = 8 hours
Overtime rate = $18.00 x 1½ = $27.00 per hour
Overtime pay = 8 x 27.00 = $216.00
Total earned for the week = $684.00 + $216.00 = $900.00

Example 2:
Izabella earns a salary of $35880. If she works 46 hours in a week, how much does she get paid for that week?

Izabella gets the same amount each week regardless of the number of hours worked.
Weekly installment = $35880 ÷ 52 = $690 i.e. total earned for the week = $690

Exercise:
Q.1. Morgan is paid $20.00 per hour for a 38 hour week. If he works 50 hours in a week with overtime being paid at time-and-a-half, how much does he earn for the week?

Q.2. Elizabeth earns a salary of $48880. If she works 48 hours in a week, how much does she get paid for that week?

Q.3. Jerry is paid $18.00 per hour for a 40 hour week. If he works 52 hours in a week with 8 hours overtime being paid at time-and-a-half and the rest at double-time, how much does he earn for the week?

Q.4. Mary is paid $22.00 per hour for a 37½ hour week (5 days @ 7½ hours per day). Mary works for 8½ hours on Monday, 9 hours on Tuesday, 7½ hours on Wednesday, 9½ hours on Thursday and 10 hours on Friday.
(i) What is Mary's normal pay (without overtime) for the week?
(ii) How many hours overtime did Mary work?
(iii) If Mary is paid time-and-a-half for her extra hours, what is the amount of her overtime pay?
(iv) How much was Mary paid for the week?

Answers: Q.1. $1120 Q.2. $940 Q.3. $1080 Q.4. (i) $825.00 (ii) 7 hours (iii) $231.00 (iv) $1056

CONSUMER ARITHMETIC 1

Q.1. Mary earns $12.50 per hour and time-and-a half for overtime. How much does she earn in a week where she works 40 hours at regular time plus 10 hours overtime?

Q.2. Tom earns $640 per week. How much does he get if he gets his four weeks holiday pay with 17˝% loading?

Q.3. Heidi earns $728 for a 40 hour week plus 8 hours overtime. If she is paid time-and-a-half for overtime what is her normal hourly rate of pay?

Q.4. The Ripemoff department store used to sell walkmans for $80.00. The manager raised the price by 20% and then advertised “20% discount” on the new price. How much would a customer now pay for a walkman?

Q.5. Stephanie bought a top for $49.50 which consists of the sale price plus 10% GST. What is the sale price?

Q.6. Sophie placed $800 in a term deposit at the bank. If her money earned 6% simple interest for 3 years how much was her final bank balance?

Q.7. Bob bought a T.V. for $5800 on time payment over 3 years at 10% simple interest.
(i) How much interest did Bob pay?
(ii) What was the total amount Bob paid for the T.V.?
(iii) What was the amount of Bob’s monthly repayments (to the nearest 5 cents)?

Q.8. Lisa earned $16.80 per hour for a 40 hour week. Tax of $134.40 was deducted from her gross wage. Also 8% of her gross wage was paid into a special superannuation account.
(i) How much superannuation did Lisa pay for the week? (ii) How much did Lisa receive in her pay packet (to nearest 5 cents)?

Q.9. (i) Write down the formula for compound interest.
(ii) Bert invested $1000 at 6% compound interest for 10 years. What was his investment worth at the end of this time?
(iii) Simone invested $1000 at 7% simple interest for 10 years. What was her investment worth at the end of this time?

Q.10. Becky was paid $2538 that consisted of 3 weeks pay plus a 17˝% holiday loading. What was Becky’s weekly rate of pay?

ANSWERS:

Q.1. $687.50 Q.2. $3008 Q.3. $14 Q.4. $76.80 Q.5. $45.00 Q.6. $944 Q.7. (i) $1740 (ii) $7540 (iii) $209.45 Q.8. (i) $53.76 (ii) $483.85 Q.9. (i) A = P ( 1 + r/100 )n where A = final amount P = principal r = rate % n = number of compounding periods, usually years. (ii) $1790.85 (iii) $1700 Q.10. $720

CONSUMER ARITHMETIC 2

Q.1. David earns $13.00 per hour and time-and-a half for overtime. How much does he earn in a week where he works 40 hours at regular time plus 10 hours overtime?

Q.2. Jordan earns $720 per week. How much does he get if he gets his four weeks holiday pay with 17½% loading?

Q.3. Izabella earns $736 for a 40 hour week plus 4 hours overtime. If she is paid time-and-a-half for overtime what is her normal hourly rate of pay?

Q.4. The Ripemoff department store used to sell ipods for $900.00. The manager raised the price by 30% and then advertised “30% discount” on the new price. How much would a customer now pay for an ipod?

Q.5. Melanie bought a top for $38.50 which consists of the sale price plus 10% GST. What is the sale price?

Q.6. Julie placed $600 in a term deposit at the bank. If her money earned 5% simple interest for 4 years how much was her final bank balance?

Q.7. Alfred bought a T.V. for $3600 on time payment over 3 years at 10% simple interest.
(i) How much interest did Alfred pay?
(ii) What was the total amount Alfred paid for the T.V.?
(iii) What was the amount of Alfred ’s monthly repayments (to the nearest 5 cents)?

Q.8. Thi earned $18.80 per hour for a 40 hour week. Tax of $163.20 was deducted from her gross wage. Also 9% of her gross wage was paid into a special superannuation account.
(i) How much superannuation did Thi pay for the week? (ii) How much did Thi receive in her pay packet (to nearest 5 cents)?

Q.9. (i) Write down the formula for compound interest.
(ii) Colin invested $1000 at 5% compound interest for 10 years. What was his investment worth at the end of this time?
(iii) Eva invested $1000 at 5½% simple interest for 10 years. What was her investment worth at the end of this time?

Q.10. Marilyn was paid $3807 that consisted of 4 weeks pay plus a 17½% holiday loading. What was Marilyn ’s weekly rate of pay?

ANSWERS:

Q.1. $715 Q.2. $3384 Q.3. $16 Q.4. $819 Q.5. $35.00 Q.6. $720 Q.7. (i) $1080 (ii) $4680 (iii) $130.00 Q.8. (i) $67.68 (ii) $521.10 Q.9. (i) A = P ( 1 + r/100 )n where A = final amount P = principal r = rate % n = number of compounding periods, usually years. (ii) $1628.89 (iii) $1550.00 Q.10. $810

More About Income

Employees do not get to keep all of their pay. Some of it is deducted to pay income tax. There are also other things that can be deducted from a worker's pay such as medical insurance, union subscriptions and superannuation.

The amount a worker is paid before any deductions have been made from their pay is called Gross Pay.
The amount that the worker receives in their pay-packet or pay cheque is called Net Pay. It is the gross pay minus all of the deductions.

Some workers such as sales people are paid on Commission i.e. they receive a percentage of the price of the goods they sell or a percentage of the profits.
Sometimes employees are paid a retainer (a fixed amount regardless of their sales or profits) and a commission.

Some workers such as those who work at home are paid Piecework i.e. they are paid a fixed amount for each item or task completed.

Australian wage and salary earners are also paid a 17½% Leave Loading for some or all of their annual holidays. This means that they get their normal pay for the holidays plus an extra 17½%.

Exercises:
Q.1. Carol sells books and receives 22½% commission. If her sales for the week are $4800, how much does Carol earn?

Q.2. Ray is paid $24.50 per hour for a 38 hour week. He pays $126.40 tax and 5% of his gross pay into a superannuation fund.
(i) How much is Ray's gross pay?
(i) How much superannuation does Ray pay?
(ii) What is Ray's net pay?

Q.3. Kevin works for a real estate firm that pays him a retainer of $500 per week plus a commission of 0.5% of the price of the property that he sells. Over a four week period Kevin sold a home unit for $280 000 and a house for $460 000. How much did Kevin earn for the four weeks?

Q.4. Maureen sews blouses at home. She is paid 95 cents per blouse. If each blouse takes 4 minutes to sew, how much would Maureen earn for a 38 hour week?

Q5. Sophie earns a salary of $50440. She is about to take her annual holidays and her pay will consist of 4 weeks pay plus a 17½% holiday loading. How much will Sophie be paid for the four weeks?

Q.6. Mia operates a stall in a shopping mall. She is paid $580 per week plus 5% of all sales over $2000. If Mia sells $4200 worth of goods in a week, how much is she paid?

Q.7. Jordan is paid $23.50 per hour for a 38 hour week. He pays $138.60 tax, $18.40 medical insurance and 6% of his gross pay into a superannuation fund.
(i) How much is Jordan's gross pay?
(ii) What is Jordan's net pay? (to nearest 5 cents)

Answers: Q.1. $1080 Q.2. (i) $931 (ii) $46.55 (iii) $758.05 Q.3. $5700 Q.4.$541.50 Q.5. $4559 Q.6. $690 Q.7. (i) $893 (ii) $682.40

INTEREST

Simple Interest: I = (Prn)/100 where I = Simple Interest P = Principal, r = rate per interest period (usually a year), n = number of interest periods.

Example: What will be the value of $2000 invested for 5 years at 6% p.a. simple interest?
I = (Prn)/100 = 2000x6x5/100 = 600 Amount = Principal + Interest = $2000 + $600 = $2600

Exercises 1:
Q.1. If I invest $600 at a simple interest rate of 7% p.a., how much will I have in the account after 10 years?

Q.2. Ryan invested $50 in a bank account that paid 4% p.a. simple interest. How much would it be worth after 9 months?

Q.3. What simple interest rate would be required to double the amount of the investment in 20 years?

Compound Interest: A = P(1 + r)n where A = final amount, P = Principal, r = rate As a decimal,per interest period (usually a year), n = number of interest periods.
Compound interest is where you earn interest on your interest.

Example: What will be the value of $2000 invested for 5 years at 6% p.a. compound interest?
A = p(1 + r)n = 2000(1 + 0.06)5 = 2000(1.06)5 = $2676.45

Exercises 2:
Q.1. If I invest $600 at a compound interest rate of 7% p.a., how much will I have in the account after 10 years?

Q.2. Josh invested $50 in a bank account that paid 4% p.a. compound interest. How much would it be worth after 5 years?

Q.3. Chris invested $5000 for 6 years at 6% p.a. compound interest. What was the final value of the account?

Q.4. Karen invested $5000 for 6 years in an account where the 6% p.a. interest was compounded every 6 months. What was the final value of the account?

Q.5. Bob's house is worth $500 000. The real estate agent told Bob that values were increasing at 6% per annum. If the estate agent is right and values are increasing at 6% compounded annually, how long will it be before Bob's house doubles in value and makes him a millionaire?
(answer to nearest year)

Answers: Ex.1 Simple Interest: Q.1. = $1020 Q.2. = $51.50 Q.3. = 5% Ex. 2. Compound Interest: Q.1. = $1180.29 Q.2. = $60.83 Q.3. = $7092.60 Q.4. = $7128.80 Q.5. 12 years

INTEREST 2

Compound Interest: A = P(1 + r)n where A = final amount, P = Principal, r = rate as a decimal, per interest period (usually a year), n = number of interest periods.
Compound interest is where you earn interest on your interest.
Example: What will be the value of $5000 invested for 10 years at 5% p.a. compound interest?
A = P(1 + r)n = 5000(1 + 0.05)10 = 5000(1.05)10 = $8144.47

Exercises: Q.1. If I invest $200 at a compound interest rate of 8% p.a., how much will I have in the account after 10 years?

Q.2. Josh invested $100 in a bank account that paid 5% p.a. compound interest. How much would it be worth after 4 years?

Q.3. Chris invested $10 000 for 20 years at 6% p.a. compound interest. What was the final value of the account?

Q.4. Karen invested $10 000 for 20 years in an account where the 6% p.a. interest was compounded every 6 months. What was the final value of the account?

Q.5. Michelle invested $10 000 for 20 years in an account where the 6% p.a. interest was compounded every month. What was the final value of the account?

The compound interest formula can also be used to determine depreciation. In this case the rate is subtracted.

Depreciation: A = P(1 - r)n where A = final value, P = Initial cost, r = rate per depreciation period (usually a year), n = number of depreciation periods.

Example: A photocopier costs $4 000 and depreciates at the rate of 20% per year. How much is it worth after 5 years?
A = P(1 – r)n 4000(1 – 20/100)5 = 4000(0.8)5 = $1310.72

Exercises.
Q.1. Simone bought a walkman for $120. If it depreciates at the rate of 15% per year, how much is it worth after 3 years?

Q.2. Emma bought a car for $8000. If it depreciates at the rate of 12% per year, how much will it be worth after 10 years?

Q.3. Lauren bought a sound system for $3 800. If it depreciates at the rate of 1% per month, how much will it be worth after 2 years?

Answers:
Compound Interest: Q.1. = $431.78 Q.2. = $121.55 Q.3. = $32071.35 Q.4. = $3260.38 Q.5. = $33102.04
Depreciation: Q.1. = $73.70 Q.2. = $2228.01 Q.3. = $2985.58

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