# Math Week 3 Critical Thinking: Mathematical Explorations (Essay Sample)

Option #1: Consumer Mathematics #1

Question #1 – Simple Interest

Jack borrowed money to finance his new business. Private investors offered Jack $28,000 of the $35,000. To make up the difference, Jack secured a small business, simple interest loan. Jack’s loan was structured as an installment loan that required him to pay $297.50/month for 30 months. Calculate the amount financed, total installment price, the finance charge, and the interest rate.

Question #2 – Annuity Payment

Jason is saving money for a down payment on a racing bicycle. He needs $2,000 in one year to make his down payment and is investing in an annuity yielding an annual interest rate of 4% compounded monthly. If the annuity requires that Jason make monthly investments, what annuity payment must Jason make to save enough for his bicycle down payment?

Question #3 – Mortgage Financing

Zoe purchased a $129,000 home with 30-year term, 6% rate mortgage. At closing she paid a $10,000 down payment, requiring her to purchase private mortgage insurance (PMI) at a cost of $25 per month. Calculate Zoe’s monthly mortgage plus PMI payment.

Requirements:

Show all your work so that the instructor clearly sees how you solved the problem.

Make sure your final answer is clear and visible.

Paper must be written in 3rd person.

Your paper should be about 4-5 pages in length or longer (counting the title page and references page) and cite and integrate at least one credible outside source. The CSU-Global Library(Links to an external site.)Links to an external site. (Links to an external site.) is a great place to find resources. Your textbook is a credible resource.

Include a title page, introduction, body, conclusion, and a reference page.

The introduction should describe or summarize the topic or problem. It might discuss the importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic.

The body of your paper should answer the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.

The conclusion should summarize your thoughts about what you have determined from the data and your analysis, often with a broader personal or societal perspective in mind. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.

Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.

Math Week 3 Critical Thinking

Name

MTH109-1 – Mathematical Explorations

Colorado State University – Global Campus

Instructor

Date

Introduction

For borrowers and the lenders, the simple interest rate, compound interest rate and annuity payments are some of the considerations to determine the cost of borrowing. The simple interest for capital (loan or savings) is directly proportional to the initial capital, at a specie period of time and at a specific interest rate. When interest is capitalized in compound interest, the interest calculated in each period is added to the capital or the previous balance (Brigham & Ehrhardt, 2018). The compounding interest approach is common in bank loans and savings to determine the value of savings and loan balance. In this approach, the interest is added to the balance or savings balance and the new interest is calculated on the loan balance or saving, which makes the interest value increase month by month. This is an analysis of the simple interest, annuity payment and mortgage financing.

Simple Interest

The simple interest measures the cost of a loan and since private investors have offered $ 287,000, the balance of $ 7,000 to get the required $ 35, 000 is required. The loan is to be paid in 30 months for $297.50/month, which equals to $8,925. Thus, the total amount accrued, principal plus interest, from simple interest on a principal of $7,000.00 at a rate of 11% per year for 2.5 years is $8,925. Using the simple interest, the interest is not added to the initial capital once the term of the investment or credit has expired. The amount financed is used to determine the interest rate and the rate is directly related to the finance charges (Park, 2013). The interest rate provides a balance between the risk and the potential gain on a certain amount of money in a specific situation and time.

Amount financed: $35,000 – $28,000 = $7,000

Total Installment price: $297.50 x $30 = $8,925

Finance charge: $8,925 – $7000 = $1,925

30 months is 2 ½ years

The simple interest equation (Principal + Interest)

Where A = P (1 + rt) or and I = Prt

A = Total Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

r = Rate of Interest per year = R/100

t = Time Period involved in months or years

A = P (1 + rt) 7,000(1+2.5r) where r= 1925/17500 0.11 or 11%

Using the initial amount invested the interest rate is calculated and does to vary with time unlike the compound interest. There is no capital increase and the interest rate was determined to be 11%, which implies that the amount of money generated per year for the investment is $11 per $100 financial investment. The simple interest is not considered as reinvested capital, and this explains why the investment remains at 11%. The interest applied to the investment or saving depends on what is initially invested or saved, the time period expressed in years and the interest earned.

Annuity Payment

Jason requires the $ 2,000 for bicycle payment after investing in an annuity that

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