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CSEC Mathematics: Consumer Arithmetic

Sales Tax

A sales tax is a consumption tax imposed by the government on the sale of goods and services. Some of you may be familiar with Government Consumption Tax (GCT) or Value-Added Tax (VAT), which are usually expressed as a percentage of whatever is being purchased.

To find the sales tax on a certain item, you will usually be given the marked price and the sales tax percentage:

Sales tax = MP x (% sales tax/100)


To find the selling price overall with the given information:

SP = MP + Sales tax


Example 1: You are in the UK and purchase a box of Maltesers with a marked price of $5. However, the UK has a VAT of 20%. What is the selling price of the product?

VAT = MP x (% VAT/100)

= $5 x (20/100)

= $1


SP = MP + VAT

= $5 + $1

= $6

You pay $6 for the Maltesers.


Example 2: You buy three beef patties with a marked price of $420.00 dollars but a selling price of $489.30 when sales tax was applied. What is the sales tax percentage?

You first calculate the sales tax:

Sales tax = $489.30 - $420.00

= $69.30

You then find the percentage sales tax by expressing the sales tax as a fraction of the marked price:

% Sales tax = ($69.30/$420.00) x 100

= 16.5%

The sales tax is 16.5%.


Loss

If something is sold for less than it was purchased for, it is considered to be sold at a loss.

Loss= CP-SP

(CP is cost price, or the amount for which the item was originally purchased or produced)

The loss is often expressed as a percenage:

% Loss = (Loss/CP) x 100


Example 3: To capitalize on the Christmas rush, you purchase all the Barbie dolls in you local toy store in hopes of selling them for a markup. In total, you spend $57,000.00 on 30 dolls. However, you are only able to resell all of them to an eccentric collector for $45000.00. What is your loss?

Loss = CP-SP

= $57000.00-$45000.00

= $12000.00

You lost $12000.00.


b) What is your percentage loss?

% Loss = (Loss/CP) x 100

= ($12000.00/$57000.00) x 100

= 21.1% (1 d.p.)

Your percentage loss was 21.1%.



Profit

Most commodities are sold at profit, i.e. they are sold for more than their original cost.

Profit= SP-CP

And in percentage form:

% Profit= (Profit/CP) x 100

Example 4: Your friend purchased a bundle of 50 stickers in the US for the equivalent of $10 each. He returns and sells them around his school for $50 each. What is his profit for one sticker?

Profit= SP-CP

= $50 - $10

= $40

Your friend makes a profit of $40 per sticker.

b) What is his percentage profit?

%Profit = ($40/$10) x 100

= 400%

Your friend makes a profit of 400%.


Hire Purchase

Hire purchase involves making payments for something in installments. You are able to use the item you are paying for before you are done paying for it. You make an initial payment, known as a down payment, before making additional contributions towards the outstanding balance of the product over a fixed time period at regular intervals (eg monthly for 16 months, etc). . The interest on a hire purchase loan is always charged at a simple interest rate and only charged on the amount owing, or the outstanding balance.

It is important to note that making a hire purchase payment is usually more expensive in total than paying for it up front with cash.


Example 5: Sue bought a Livng-room Set on a hire purchase plan. The cash price is $3600. On the hire purchase plan, she must pay $700.00 as a down payment plus 20 payments of $200.00 monthly.

Calculate:

a) the total monthly payments.

Total monthly payments= number of payments x price of each payment

= 20 x $200.00

= $4000.00


b) the total cost of the set on the hire purchase plan.

Total hire purchase cost of the set = total monthly payments + down payment

= $4000.00 + $700.00

= $4700.00


c) her savings if she had bought it cash.

Savings if she had bought with cash = total hire purchase cost of the set- cash price

= $4700.00 - $3600.00

= $1100.00


d) The interest charged

First, we subtract the deposit amount from the cash price:

$3600.00-$700.00 = $2900.00

We then subtract this value from the total monthly payments of the hire purchase plan:

Interest = $4000.00 - $2900.00

= $1100.00

We can go further to calculate the percentage interest:

% Interest = ($1100.00/$2900.00) x 100

= 37.9%


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