Math Week 3 Critical Thinking: Mathematical Explorations

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 yields 4% compounded monthly and will make monthly payments to achieve this. For the annuity payment in one year’s time is $2,000 and this is the future value as it is the total value required at the end of the period capital. When the interest is compounded monthly, this is 4%/ 12= 0.33% for 12 months. Unlike simple interest, there is interest capitalization in compound inter...