Part 2 Finite Mathematics Chapter 3 Mathematics of Finance Chapter 4 System of Linear Equations; Matrices
Chapter 3 Mathematics of Finance Section 1 Simple Interest Section 2 Compound and Continuous Compound Interest Section 3 Future Value of an Annuity; Sinking Funds Section 4 - Present Value of an Annuity; Amortization Section 1 Simple Interest
Introduction How do I choose the right loan for a college? Would it better to take the dealer s financing or the rebate for my new car? Should my parents refinance their home mortgage? Notes: - You will need a calculator with logarithmic and exponential keys - No graphic calculator required - Review Appéndix B-2 - Additional Material: Blackboard Learn 9.1 - Reminder: percentages, as in interest rates, must be converted to a decimal form before they are used in a formula - Important remainder. To work the assignments. 3
Introduction What, are according to your own experience, the justifications to decide to accept a bank loan? 4
Introduction What, are according to your own experience, the justifications to decide to accept a bank loan? 1. Rate of interest 2. Number of down payments (time) 3. Monthly payment 4. APR 5. Additional offers (airway tickets, hotel staying, deluxe features) 6. Clerk s kindness 7. Prestige, good-will, strongest of the financing institution 8. Customer service 9. Pleasure of enjoying something new and desired (home, car, etc.) 10. All the previous ones 5
Learning Objectives for Section 3.1 Simple Interest The student will be able to compute simple interest using the simple interest formula. The student will be able to solve problems involving investments and the simple interest formula. 6
Table of Content The Simple Interest Formula Simple Interest and Investments 7
Terms principal interest /interest rate simple interest present value future value 8
The Simple Interest Formula Used in short term notes Basis for most of the material developed in this chapter Definition: I = Prt where I = interest earned P = principal (amount invested) r = interest rate (as a decimal) t = time 9
An Example Find the interest on a boat loan of $5,000 at 16% for 8 months. 10
Example Find the interest on a boat loan of $5,000 at 16% for 8 months. Solution: Use I = Prt I = 5,000(0.16)(0.6667) (8 months = 8/12 of one year 0.6667 years) I = $533.33 11
Total Amount to Be Paid Back The total amount to be paid back for the boat loan would be $5000 plus the interest of $533.33, for a total of $5,533.33. 12
Present Value and Future Value Simple Interest A = P + Prt = P (1 + rt) where A = amount, or future value P = principal, or present value r = annual simple interest rate (as a decimal) t = time in years 13
Total Amount Due on a Loan Find the total amount due on a loan of $600 at 16% interest at the end of 15 months. 14
Total Amount Due on a Loan Find the total amount due on a loan of $600 at 16% interest at the end of 15 months. Solution: A = P (1 + rt) A = 600(1+0.16(1.25)) A = $720.00 15
Present Value of an Investment If you want to earn an annual rate of 10% on your investment, how much (to the nearest cent) should you pay for a note that will be worth $5,000 in 9 months? 16
Present Value of an Investment If you want to earn an annual rate of 10% on your investment, how much (to the nearest cent) should you pay for a note that will be worth $5,000 in 9 months? Solution: A = P (1 + rt) 5,000 = (1.075)P P = $4,651.16 17
Simple interest and Investments Interest Rate Earned on a Note What is the annual interest rate earned by a 33-day T-bill with a maturity value of $1,000 that sells for $996.16? 18
Interest Rate Earned on a Note Solution Solution: Use the equation A = P (1 + rt) 1,000 = 996.16 33 1 r 360 1000 = 996.16(1+r(0.09166)) 1000=996.16+996.16(0.09166)r 1000-996.16 996.16(0.09166) r 0.042 4.2% r We normally use 360 days for a financial year 19
Another Application A department store charges 18.6% interest (annual) for overdue accounts. How much interest will be owed on a $1080 account that is 3 months overdue? 20
Another Application solution A department store charges 18.6% interest (annual) for overdue accounts. How much interest will be owed on a $1080 account that is 3 months overdue? Solution: I = Prt I = 1080(0.186)(0.25) I = $50.22 21
Interest on an Investment An investor purchases 50 shares oh a stock at $47.52 per share. After 200 days, the investor sells the stock for $52.19 per share. Using the Table 1 - Commission Schedule below, find the annual rate of interest earned by the investment. Express the answer as a percentage, correct to three decimal places. Table 1 Commission Schedule Principal Commission $0-$2,499 $29 + 1.6% of principal $2,500-$9,999 $49 + 0.8% of principal $10,000+ $99 + 0.3% of principal 22
Interest on an Investment Solution: The principal referred in the table is the value of the stock. The total cost for the investor is the cost of the stock plus the commission: 47.52(50) = $2,376 Principal 29 + 0.016(2,376) = $67.02 Commission, Table 1 2,376 + 67.02 = $2,443.02 Total investment When the stock is sold, the commission is subtracted from the proceeds of the sale and the remainder is returned to the investor: 52.19(50) = $2,609.50 Principal 49 + 0.008(2,609.50) = $69.88 Commission, Table 1 2,609.50-69.88 = $2,539.62 Total investment 23
Interest on an Investment Solution (continued): Using the formula for the Simple Interest with A = 2,539.56; P = 2,443.03; and t = 200/360 = 5/9, we have: A = P (1 + rt) 2,539.62 = 2,443.02(1 + [5/9]r) 2,539.62 = 2,443.02 + 1,357.23r 96.60 = 1,357.23r r = 96.60/1,357.23 r = 0.07117 or 7.117% 24
Chapter 3 Mathematics of Finance Section 1 Simple Interest END Last Update: Marzo /2013