Number Sense, Estimation, and Financial Computations - Paper Example

2021-08-23 10:25:19
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University of California, Santa Barbara
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Problem solving
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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. Submit this modified Answer Form in the Unit 2 IP Submissions area.

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.

First letter of your last name Possible range values for P

AF $4,000$4,999

GL $5,000$5,999

MR $6,000$6,999

SZ $7,000$7,999

Add your chosen value here:

Total value of the appliances, P $ 7500.00

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, and convert your answer into decimal form.

Annual interest rate in decimal form, r 0.15

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.)

Interest, I $3,375.00

Show and explain your work here:

Simple interest is obtained by multiplying the principal, interest rate, and time period

Thus, Interest = Principal * Rate * Amount

Interest = 7500 * 0.15 * 3

I = $3,375.00

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

Total bill (simple interest) $

Show and explain your work here:

Total bill s equal to the principal plus interest accumulated over the three-year period.

Therefore, total bill = Principal + Interest

Total bill = 7500.00 + 3375.00 = $10,875.00

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.)

Total bill (compound interest) $

Show and explain your work here:

The formula for Total Amount when using compound interest is given by the following formula:

A=P (1+ rn)ntWhere:

A = Total Bill

P = Principal

r = Interest Rate in decimals

t = time in years

n = number of times interest is compounded per year

In this case, the interest is compounded daily so n = 365

A=7500 (1+ 0.15365)365*3A=7500 (1.000411)1095Total Bill, A = $11,761.78

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

Interest, I $

Show and explain your work here:

Total interest is obtained by subtracting the principal amount from the total bill

I = A P

I = 11,761.78 7500.00

Total Interest, I = $4,261.78

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

Based on the results of the calculations, one major difference between the two is that compound interest results in a much higher total bill as compared to simple interest. The other thing is that in simple interest, the interest accumulates on the principal amount for the entire period while in compound interest, the interest accumulates based on the principal plus the interest that accumulated previously.

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

I do not think that a deferred billing option is helpful for customers since they will end up paying an amount that is more than the price of the item. This is because they will be charged interest after a certain period.

SAVING FOR 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 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:

There are several expenses that people face in retirement. Among the major ones include housing, food and beverages, transportation, and medical expenses. According to Forbes, housing accounts for most of the expenses in retirement at 46.89%. This is followed by food and beverages which account for 15%, transportation 13.82%, and finally medical care that accounts for 12.1% of the total expenses in retirement. As such, it is important for one to consider these expenses and plan ahead so as to be comfortable in old age.

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.

Future value, F $1,000,000

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

Time, t 30

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, and convert this to its decimal form.

First letter of your last name Possible values for r

AF 5.00%6.99%

GL 7.00%8.99%

MR 9.00%10.99%

SZ 11.00%12.99%

Add your chosen value here:

Annual interest rate in decimal form, r 0.12

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.

Compounding Period n

Yearly 1

Semi-Annually 2

Quarterly 4

Monthly 12

Weekly 52

Add your chosen value here:

Compounding Period, n 4

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=rn Round your answer to 6 decimal places.

Interest rate per compounding period, i 0.03

Show and explain your work here:

Interest rate per compounding period is found by dividing the annual interest by the compounding period. The annual interest is 12% and the compounding period is 4. Therefore,

i= rn= 0.124=0.03Your contribution per period, which you will denote by C, to this retirement account is calculated using the following formula:

C=F*i1+i(n*t)-1.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.

Contribution amount, C $17,321.96

Show and explain your work here:

C= F*i(1+in+t-1)= 1,000,000*0.03(1+0.034+30-1)= 30,0001.0334-1=$17,321.96Calculate your total contribution to this retirement account, which you will denote by TC, by using the formula TC = C x n x t.

Total contribution, TC $2,078,635.20

Show and explain your work here:

TC = C * n * t = 17321.96 * 4* 30

= $2,078,635.20

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:

There is a difference in value between the total contribution and the lumpsum that will be received. Based on this calculation, this difference is 1,078,635.20 which is more than the lumpsum that will eventually be received. This difference is known as amortization.

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

Show and explain your work here:

Planning for retirement important since it allows one to have a good quality of life and cater for all the expenses that may arise during the retirement years. Preparing for retirement allows one to take care of unforeseen medical expenses, live in a good home, and deal with the financial changes that may come during the retirement years (Elemeraji, n.d). As such, it is evident that retirement planning is essential in allowing one to live a good quality life after retirement.

References

Anderson, N. (2015). Forbes Welcome. Forbes.com. Retrieved 5 January 2018, from https://www.forbes.com/sites/nancyanderson/2015/03/01/the-biggest-expenses-in-retirement-and-how-to-prepare-for-them-now/#2ef0e23e22b9

Elmerraji, J. Retirement Planning: Why Plan For Retirement?. Investopedia. Retrieved 5 January 2018, from https://www.investopedia.com/university/retirement/retirement1.asp

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