# Business math of interest rates and formulas

Solve the following problems showing all your work every step of the way.

1. You have been given information that if a student is a resident and they enroll for more than 12 hours, then their tuition will equal $120 plus $10 per hour for every hour greater than 12. Create an equation that would allow a student to simply plug in their number of hours enrolled and calculate their tuition. Give a specific example to show your equation works.

2. Research: There are many formulas that are used in our everyday lives. Use the library or the internet to research an example of a formula, explain the variables of the formula, and show a specific example by plugging in values for the particular formula.

3. Set up three different equations that have the solution of 8. Solve your equations for your particular variable to prove the solution is 8.

4. A business buys magazines for $2.50 each and sells the same magazine for $3.50 each. How many magazines should the business sell in order to profit $125? Create an equation by letting m equal the number of magazines. Solve the equation for m.

II. Research. Research interest rates and find the reasons that interest rates rise and fall. Who sets the interest rates? The discussion should be at least two paragraphs long with at least two sources.

III. You have received an invoice for computer equipment. On the invoice you have ordered 35 servers for a list price of $1200 each. The invoice shows a trade discount series of 3/8/5. Find the net price and the discount of the computer equipment.

IV. The same invoice in part III, gives another option of a total of 16% discount. Are the net prices and the discount for the computer equipment the same? Explain.

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#### Solution Preview

1) Let x represent the number of hours enrolled.

If x<= 12, then the tuition is 120

If x > 12, then the tuition is 120 + 10 * (x - 12)

Suppose the a student enrolls in 18 hours, since 18 > 12, the tuition is then

120 + 10 * (18 - 12) = 120 + 60 = 180

2) One of our daily life formula example is the Fahrenheit and Celsius Conversion Formulas

C = (F - 32) * 5/9

where C is degree Celsius and F is degree Fafrenheit. So if we want to find out what is the corresponding degree Celsius for 86 degree Fahrenheit, we would plug F = 86 into the above formua. We get

C = (86 - 32) * 5/9

= 54 * 5/9

= 30 degree Celsius

3)

first equation x + 6 = 14

To solve for x, we minus 6 on both sides of the equation, we get

x + 6 - 6 = 14 - 6

x = 8

second equation 2x = 16

To solve for x, we divide 2 on both sodes of the equation, we get

2x / 2 = 16/2

x = ...

#### Solution Summary

This provides several examples of working with business math applications, including net prices and discount, interest rates, equations, and research.

Business Mathematics: Compound Interest and Investment Advice

Individual Work 1

Consider the concept of compound interest you read about this week. Now, apply your knowledge of these models to a practical problem.

Please respond to all of the following prompts in the class discussion section of your online course:

1. You have been asked by your friend to describe this topic. Your friend knows very little about math, but learns well with pictures and analogies. Come up with a creative way to explain the concept of "compound interest" to your friend.

2. Go to http://bankrate.com/brm/calc/savecalc.asp. If you want to save $25,000 for a down payment on a house and you have ten years to save this amount, how much would you need to save monthly to achieve this goal if the interest rate is 5% compounded monthly. What happens if you can increase your interest rate to 8%? NOTE: Enter $100 for the "How much money can you spare for your first deposit or investment".

3. Develop a personal example of compound interest that differs from the example in question 2.

Individual Work 2

Scenario: A client comes to you for investment advice on his $500,000 winnings from the lottery. He has been offered the following options by three different financial institutions and requests assistance to help understand which option would be the best for his investment.

- Option 1: 6% compounded interest quarterly for 5 years.

- Option 2: 8% compounded interest annually for 5 years.

Write a professional memo that covers the following information:

a. Explain to the client the main differences between simple interest versus compound interest.

b. Explain the results of the three different options by showing the client the step-by-step calculations.

c. Explain which investment option is better for your client and why.

The total minimum document length should be one page.