Problem Set #1
ALL work must be shown/explained to receive credit. You are only allowed to submit your problem set ONCE so make sure to check all your work before submission. Submission by e-mail is not allowed.
*My goal for this problem set is for my students to not ONLY understand the correct calculations, but to also understand its applications in real life scenarios. I hope that you will find this educational and useful, either personally or professionally. As I have mentioned in Blackboard, no matter how well you know the calculations, if you do not know how to explain your results, then the message conveyed is that the student was confused and did not have a clear understanding of the topic.
QUESTION 1 (30 PTS)
According to a research, the population of Japan x years after the year 2010 can be modeled by
, where y: is the number of people (in millions).
- Using this model, predict the population of Japan by completing the table below. (Round all final answers to two decimal places).
|YEAR||x-values||y-values (in millions)|
- Create a SCATTER graph of this data using Microsoft Excel and paste your graph below.
- Now, do your research and check the current population of Japan. Based on your research, do you think this is a good mathematical model in predicting the country’s population? Why or Why not?
|Date of Research (when did you get your data): Current Population: Reference for your data: Analysis of data in comparison to the mathematical model. Why do you think it is important to know the trend of a country’s population? Provide a brief analysis below.|
QUESTION 2 (30 PTS)
Recently, the concept of “buy now, pay later” is increasingly getting popular. This allows shoppers to buy things now without paying the bill at checkout.
Assume you buy a new set of furniture and decors for your new apartment. You are given the provision that you do not need to pay the bill at checkout and as long as you pay it within the next two years from the date of purchase, no interest will be charged. However if you are even one day late in paying the bill, the store will charge you interest for the past 2 years.
Suppose you forget about the bill and pay it one day late.
CHOOSE A NUMBER BETWEEN $5,000 and $9,000 for the value of the furniture and decors. This will be your Principal Amount, P. It does not necessarily have to be a whole number.
P = $______________
Now, answer the following questions and round your answer to the nearest cent.
- How much interest will you pay if the store charges you 26.25% simple interest at t = 2 years?
How much is your total bill – the value of the appliance plus the interest?
SHOW YOUR WORK BELOW:
- How much is your total bill if, instead, the store charges you 26.25% interest compounded daily at t=2 years?
How much compound interest will you pay?
SHOW YOUR WORK BELOW:
- Compare and analyze the results of your calculations from questions (a) and (b). Which interest is higher?
- Provide a COLLEGE LEVEL analysis of the pros and cons of this provision. Have you tried this “buy now, pay later” option? Do you think this option of deferred billing is good for shoppers?
QUESTION 3 (30 PTS)
Suppose you have $5,000 to invest for the next 40 years. You are given 3 choices on where to invest your money.
|Account #1||12.20% compounded weekly|
|Account #2||12.18% compounded daily|
|Account #3||12.16% compounded continuously|
- Calculate the APR (assume P=$100, t=1 year) for each account. Round to 2 decimal places, in percent form.
SHOW YOUR WORK BELOW:
- Based on your calculations, which account will you invest your $5,000? Why? How much money will you have after 40 years in the account that you have chosen? How much in total interest will you gain? In other words, from $5,000, by how much did your money increase?
- In real life, if you have $5,000 to invest, will you make this investment? Why? If not, where would you rather invest your money?
Provide a COLLEGE LEVEL analysis below:
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