# Gen College Math

Question

MATH125: Unit 2 Individual Project

Number Sense, Estimation, and Financial Computations

Be sure to show ALL of your work details. Submit your answers in a Word document in the Unit 2 IP Submissions area.

Question 1: CONSUMER CREDIT

For big purchases, many stores offer a deferred billing option (buy now, pay later) that allows shoppers to buy things now without paying the bill at checkout.

Assume you bought new appliances for your newly renovated home. Based on the first letter of your last name, choose the total value of the appliances that you have purchased. This will be denoted by P. It does not necessarily have to be a whole number.

First letter of your last name

Possible values for P

A–F

$5,000–$5,999

G–L

$6,000–$6,999

M–R

$7,000–$7,999

S–Z

$8,000–$8,999

Total value of the appliances, P

$

The store where you bought these appliances offered you a provision that if you pay the bill within 2 years, you will not be charged any interest for your purchases. However, if you are even a day late in paying the bill, the store will charge you interest for the 2 years.

Although the annual interest rate is based on your credit worthiness, disregard this on this assignment and instead, choose an interest rate between 22% and 26%. This will be denoted by r.

Annual Interest rate in decimal form, r

Suppose you forget about the bill and pay it 1 day late. How much interest do you pay if the store charges you simple interest? Because this is a dollar value, round your answer to the nearest cent. (Assume t= 2 years.)

How much is your total bill—the total value of the appliances plus the interest? Round your answer to the nearest cent.

How much is your total bill if, instead, the store charges you interest that is compounded daily? Use 6 digits on your intermediate calculations, and round your final answer to the nearest cent. (Assume t = 2 years.)

How much interest do you pay if it is compounded daily? Round your answer to the nearest cent.

Based on the result of your calculations, write a summary about the difference between simple and compound interest.

Do you think a deferred billing option is helpful for shoppers? Explain your answer.

Question 2: Saving for Your Retirement

Suppose your goal is to have a lump sum that you can withdraw when you retire. To accomplish this, you decided to contribute a portion of your paycheck in an annuity.

Using the AIU Library or the Internet, read about what kind of expenses you will be faced with when you retire. Write a brief summary of your research.

Based on your research, state the lump sum, in U.S. dollars, that you want to have when you retire. This is the future value of your investment; denote it by F.

Future Value, F

$

State the time, in years, that you plan to contribute to your retirement account. Denote this by t.

Time, t

Based on the first letter of your last name, choose the annual interest rate for your retirement account. Denote this by r,and you will convert this to its decimal form. It does not necessarily have to be a whole number.

First letter of your last name

Possible values for r

A–F

6.00%–7.99%

G–L

8.00%–9.99%

M–R

10.00%–11.99%

S–Z

12.00%–13.99%

Annual interest rate in decimal form, r

From the table below, choose how many times per year you want to contribute to your retirement. Denote this by n, and this will also be your compounding period.

Compounding Period

n

Yearly

1

Semi-Annually

2

Quarterly

4

Monthly

12

Compounding period, n

Calculate the interest rate per compounding period, which you will denote by i, by dividing the annual interest rate from #4 by the compounding period from #5, (i.e.,

. Round your answer to 6 decimal places.

Interest rate per compounding period, i

Your contribution per period, which you will denote by C, to this retirement account is calculated using the following formula:

Using the values that you have chosen for F, i, n, and t, calculate your contribution per period. Use six decimal places for your intermediate calculations, and round your final answer to the nearest cent.

NOTE: Make sure to review exponents and the order of operations from College Math Chapter 1.

Calculate your total contribution to this retirement account, which you will denote by TC, by using the formula TC = C x n x t.

What can you say about the difference in value between your total contribution (TC) and the lump sum (F) that you will receive? Based on what you have learned in this unit, is there a term that is used for this difference?

Summarize the results of your calculations, and explain why it is important to prepare for your retirement.

Attachments

Gen_Math21.docx (24.33 KB)

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