NAME: |

**MATH125: Unit 2 ****Submission Assignment**** Answer Form**

**Number Sense, Estimation, and Financial Computations**

ALL questions below regarding CONSUMER CREDIT and SAVING FOR RETIREMENT must be answered. **Show ALL step-by-step calculations, round all ****of ****your final answers correctly****,**** and include the units of measurement**. Upload this modified Answer Form to the intellipath Unit 2 Submission lesson. Make sure you submit your work in a modified MS Word document; handwritten work will not be accepted. If you need assistance, please contact your course instructor.

First letter of your last name |
Possible range values for P |

A–F | $4,000–$4,999 |

G–L | $5,000–$5,999 |

M–R | $6,000–$6,999 |

S–Z | $7,000–$7,999 |

Total value of the appliances, P
| $5,500 |
---|

Annual interest rate in decimal form, r
| 0.14% |
---|

Interest, I
| $2310 |
---|

Total bill (simple interest)
| $7810 |
---|

Total bill (compound interest)
| $8370.11 |
---|

Interest, I
| $2870.11 |
---|

Simple Interest |
Compound Interest |

The interest is calculated as a percentage of the principal amount only. | The interest is calculated as a percentage of the principal amount and the interest which has accrued. |

In simple interest, the principal amount remains constant. | In compound interest, the principal amount continues to change during the whole borrowing period. |

The growth in simple interest remains uniform throughout. | The growth in compound interest increases rapidly over the entire borrowing period. |

The formula for simple interest isI = P×R×T | The formula for compound interest isA = P1 + rnnt |

Returns obtained from simple interest are always less. In this case, the interest was $2310 | Returns obtained from compound interest are comparatively high. In this case, the interest was $2870.11 |

Yes, I think the deferred billing option is very helpful to shoppers because the interest paid is less compared to compound interest.

**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. Using the table range values below, choose one total value for the appliances that you have purchased based on the first letter of your last name. Denote this by
*P*. It does not necessarily have to be a whole number. - Type your chosen value here:
**(****4****points)** - The store where you bought these appliances offered you a provision that if you pay the bill within 3 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 3 years.
- Choose an interest rate between 12% and 16%. Denote this by
*r**,***(****4****points)** - 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*= 3 years.) **Show and explain your work here:****(****5****points)**- I = P×R×T, where;
- P = $5500
- R = 0.14%
- T = 3
- I = 5500×0.14%×3
- I = $2310
- How much is your
**Show and explain your work here:****(****5****points)**- Total bill is calculated by adding up the value of the appliances plus the interest.
- Therefore, total bill is $5500 + $2310 = $7810
- 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*= 3 years.) **Show and explain your work here:****(****6****points)**- Compound interest formula;
- A = 5500 365×3
- A = $8370.11
- How much interest do you pay if it is compounded daily? Round your answer to the nearest cent.
**Show and explain your work here:****(****5****points)**- I = A-P
- = $8370.11- $5500
- I = $2870.11
- Based on the result of your calculations, write a summary about the difference between simple and compound interest. Explain your answer.
**(****6****points)** - Do you think a deferred billing option is helpful for shoppers? Explain your answer.
**(****5****points)**

**SAVING FOR RETIREMENT****Future value, F****$1,000,000****Time, t****35 years****First letter of your last name****Possible values for r**A–F 5.00%–6.99% G–L 7.00%–8.99% M–R 9.00%–10.99% S–Z 11.00%–12.99% **Annual interest rate in decimal form, r****0.075%****Compounding Period***n*Yearly 1 Semi-Annually 2 Quarterly 4 Monthly 12 Weekly 52 **Compounding period, n****52****Interest rate per compounding period, i****0.001442**- 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 to 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 here:
**(****6****points)**- According to my online research, I came across the expenses one is faced with during the retirement period. The major expense faced during retirement is housing and it consumes almost half of the expenses. It is imperative for one to set up a plan to pay off their mortgages early. Another expense is food and beverages whereby a lot of money will be used since food and beverages will be consumed daily. Transportation and health care are also other expenses since one will require movement from one location to another and health care expense is essential for keeping one healthy through the retirement period.
- Based on your research, state the lump sum, in $U.S., that you want to have when you retire. This is the future value of your investment; denote it by
*F*.**(****4****points)** - State the time, in years, that you plan to contribute to your retirement account. Denote this by
*t*.**(****4****points)** - Based on the first letter of your last name, choose the annual interest rate for your retirement account from the chart below. It does not necessarily have to be a whole number. Denote this by
*r*, **Type your chosen value here:****(****4****points)**- From the table below, choose how many times per year you want to contribute to your retirement fund. Denote this by
*n*, and this will also be your compounding period. **Type your chosen value here:****(****4****points)**- 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: - Round your answer to 6 decimal places.
**Show and explain your work here:****(****5****points)**- Interest rate per compounding period
- = 0.075/52
- = 0.001442
- Your contribution per period, which you will denote by
*C*, to this retirement account is calculated using the following formula:

**Contribution amount, C****$112.91****Total contribution, TC****$205,496.2**The difference between my lump sum and total contribution is $794,503.8

- Using the values that you have chosen for
*F*,*i**, n**,*and*t*, calculate your contribution per period. Use 6 decimal places for your intermediate calculations, and round your final answer to the nearest cent. **Show and explain your work here:****(****6****points)**- 1. Place numbers in the formula where they belong.
- C= 1,000,000(0.001442)/ ((1+0.001442) ^ (52 x 35) – 1)
- 2. Solve top portion
- C= 1442/ ((1+0.001442) ^ (52 x 35) – 1)
- 3. Solve parenthesis in bottom portion
- C= 1442/ ((1.001442) ^ (1820) – 1)
- 4. Solve exponent in bottom portion
- C= 1442/ (13.77078881-1)
- C=1442/12.77078881
- C= $112.9139
- Calculate your total contribution to this retirement account, which you will denote by
*TC*, by using the formula TC = C x n x t. **Show and explain your work here:****(****5****points)**- 1. Place numbers in the formula where they belong.
- TC= 112.91×52×35
- 2. Solve for TC
- TC= $205,496.2
- 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? **Show and explain your work here:****(****6****points)**

(Lump sum) $1,000,000 – (Total contribution) $205,496.2 = $794,503.8

The total contribution is less than the lump sum because the TC doesn’t have the interest included in it yet, so it is less than the lump sum by the amount of interest accrued over the period of growth. The term that can be used for the difference is accrued interest.

Based on my calculations, I would say it is essential for one to start saving for his/her retirement early enough. This is because there are a lot of important expenses which will be covered during the retirement period such as healthcare and housing. So for one to enjoy his/her retirement period, it is wiser for one t start saving early.

- Summarize the results of your calculations, and explain why it is important to prepare for your retirement.
**Show and explain your work here:****(****6****points)**

- Assume you bought new appliances for your newly renovated home. Using the table range values below, choose one total value for the appliances that you have purchased based on the first letter of your last name. Denote this by