The type of business problems accountants are confronted with are varied and complex. These can be broken down into abstract form and consequently analyzed through mathematical means. Whether it be mathematical modeling, forecasting, statistics, calculus, to name a few the need for mathematical knowledge is paramount to providing the accountant of the 21st century the necessary tools for problem solving. Accounting is a science of logic and mathematics is its language.

At its core, let us consider a simple tax payment routine which connects math and accounting:

1. A $13,000 per taxpayer basic personal exemption
2. A 17% tax rate on every dollar earned past that $13,000

Economists refer to the 17% tax rate as a marginal tax rate, as it is the percentage you have to pay when you earn an extra dollar of income.

A man earns $30,000 a year. His marginal tax rate is 17% because he earns more than $13,000. His average tax rate will be different, as he is exempt from paying taxes on the first $13,000 he earns. Thus he has to pay 17% on the remaining $17,000, which is $2890.

Average Tax Rates

1. $30K: 9.65%
2. $40K: 11.48%
3. $50K: 12.58%
4. $75K: 14.05%
5. $100K: 14.79%
6. $200K: 15.90%

Profit and Loss

An accountant takes care of the tax payments, lenders and money management for any particular company. It is important to keep track of the debtors and creditors of the company. If the creditors list is bigger than the debtors, the company’s growth may be declining. If the debtors list is bigger, the company might show a good progress in a shorter period.

Any business requires records of profit and loss. This information helps the company to make important decisions regarding their business strategy, price of their services and products, the number of people to hire, their expenses, the output rate etc.

The price at which one buys products or raw material is called the cost price.

The price at which one sells the products or services is called the selling price.

A seller gains profit if the total selling price is greater than the cost price.

Profit= Total Selling Price – Total Cost Price

Loss = Total Cost Price – Total Selling Price

Discount

When you go shopping to buy anything, the price written on the item is called the “marked price”. The price after the discount is called the “selling price”.

If the discount on a marked price is d% then the selling price = marked price – d % of marked price.

Example

What price would you pay for a garment advertised for $40 with a 20% discount?

Solution

20% of 40 = 20/100 x 40 = $8

Therefore discounted price = 40 – 8 = $ 32

Try these questions

1. Mona got a 15% discount when she bought her baby a new winter jacket. If the original price, before the discount, was $50, how much was the discount?
   Answer: 15% of 50 = $7.5
   The discount was $7.5


2. Gary earns $3000 monthly from her job at the local library. He spends $280 per month on food. What percentage of his monthly salary does he spend on food?
   Answer:
   The part of his salary that is spent on food is $280 out of his monthly salary of $3000
   = 280 / 3000 = 0.093
   = 0.093 * 100 = 9.3%
   He spends 9.3% of his salary on food.


3. The McKinley family celebrated David’s promotion with a fancy dinner in a restaurant and paid $300 for food. They also had to pay 9.5% sale tax and 10% for the tip. How much did they pay for entire the dinner?
   Answer:
   They paid for food, sales tax and tip:
   total paid = $300 + (9.5% * 300) + (10% * 300)
   $300 + $28.5 + $30 = $358.5