Sec 1 Simple Interest. Definition The amount you deposit in a bank is called the principal.

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2 Sec 1 Simple Interest Definition The amount you deposit in a bank is called the principal.

3 Sec 1 Simple Interest Definition The amount the bank pays you for the use of your money is called interest.

4 Sec 1 Simple Interest Definition Simple interest is when interest is paid only on the original principal. Interest is not earned on any earnings, reinvested or not. Note This is not how interest is paid by banks. Banks pay compound interest, that is, they pay interest on reinvested income. We will study compound interest in section two.

5 Sec 1 Simple Interest Simple Interest Formula I = Pr t I: Interest earned P: Principal r: Interest rate t: Time period

6 Sec 1 Simple Interest Example P: $5,000 r: 7.5% t: 2 years I = ( 5000)(.075)( 2) = 750

7 Sec 1 Simple Interest Example P: $5,000 r: 7.5% t: 9 months I = 9 12 ( )( ) =1080

8 Sec 1 Simple Interest There are two ways of measuring time if the time is measured in days. Exact method Ordinary method

9 Sec 1 Simple Interest Exact Method t = exact # of 365 days

10 Sec 1 Simple Interest Ordinary Method # of days = exact # of days t = 360 ( y y ) + ( m m ) ( d d )

11 Sec 1 Simple Interest Problem Find the amount of interest that $2000 deposited on June 17 th will earn if the money is withdrawn on September 10 th in the same year, and if the rate of interest is 8%.

12 Sec 1 Simple Interest Based on the Exact Method September 10 is day 253 June 17 is day 168 I = 2000 = 2000 = ( 0.08) ( 0.08)

13 Sec 1 Simple Interest Based on the Ordinary Method I = = 2000 ( 0.08) ( 0.08) 2000 = ( 9-6) + ( 10 17) 360

14 Sec 1 Future Value or Maturity Value Definition The future value or maturity value expresses the total value of the account. It is the sum of the principal and any interest earned. A = P + I = P + Pr t = P ( 1+ rt )

15 Sec 1 Future Value or Maturity Value Problem Your property tax bill is $1,200. The county charges a penalty of 11% simple interest for late payments. How much do you owe if you pay the bill 2 months late.

16 Sec 1 Future Value or Maturity Value ( rt ) A = P 1+ 2 = =1222 ( ).11

17 Sec 1 Future Value or Maturity Value Problem The maturity value of a four-month loan of $3,000 is $3,097. Find the simple interest rate.

18 Sec 1 Future Value or Maturity Value ( rt ) A = P = r = 1+ r = r = r 1 3

19 Sec 1 Stocks and Bonds Definition A share of stock in a corporation is a certificate that indicates partial ownership in the corporation.

20 Sec 1 Stocks and Bonds Definition The market value of a share of stock is the price for which a shareholder is willing to sell and a buyer is willing to purchase a share of stock in the corporation.

21 Sec 1 Stocks and Bonds Definition As an owner in the corporation, the purchaser of stock is entitled to share in corporation profits and losses. A dividend is a payment a corporation makes to its shareholders out of its earnings.

22 Sec 1 Stocks and Bonds Definition The dividend yield is the amount of dividend divided by the stock price.

23 Sec 1 Stocks and Bonds Problem Find the dividend yield for a stock that pays an annual dividend of $1.24 per share and has a current market price of $49.38.

24 Sec 1 Stocks and Bonds I = Pr t 1.24 = r 1 r =.025 = 2.5%

25 Sec 1 Stocks and Bonds Definition When a corporation issues a bond, it is borrowing money from the bondholder.

26 Sec 1 Stocks and Bonds Definition The price paid by the original purchaser of the bond is the face value.

27 Sec 1 Stocks and Bonds Definition The maturity date is the date the corporation agrees to repay the bondholder.

28 Sec 1 Stocks and Bonds Definition The coupon rate is the rate of interest that the corporation will pay the bondholder on the face value..

29 Sec 1 Stocks and Bonds It is important to observe that For a stock, there is no promise by the corporation to pay the stockholder a dividend. The interest paid on a bond is a legal obligation of the corporation.

30 Sec 1 Stocks and Bonds Problem A bond with an $80,000 face value has a 3.5% coupon rate and a 3-year maturity. What is the total of the interest payments paid to the bondholder? I = Pr t = = 8400 ( 0.035) 3

31 Sec 1 Assignment Pages , 9, 13, 19, 21, 23, 25, 29, 33, 37, 41, 45, 47, 53, 57

32 Sec 2 Compound Interest Suppose we invest $2000 at time 0 at an annual rate of 6%. A = P ( 1+ rt ) 1 0 = P + ( 1 ( 1) ) 0 r ( ) ( ) = P 0 1+ r = = 2120

33 Sec 2 Compound Interest At time 1, the principal is now $2120 and we reinvest the entire amount. At the end of the year, the value will be ( r ) A = P = = ( )

34 Sec 2 Compound Interest Definition Compound interest is where both interest and principal are reinvested. Therefore, additional interest is earned on the reinvested interest as well as the original principal.

35 Sec 2 Compound Interest Since P 1 = A 1 ( r ) A = P ( ) 1 ( 1+ r )( r ) = A 1+ r = P 1+ 0 = P ( 1+ r ) 2 0

36 Sec 2 Compound Interest Therefore, if an amount P 0 is invested at time 0 at an interest rate of r, then at time t, the accumulated value of the account is t ( r ) t A = P 1+ 0

37 Sec 2 Nominal Interest Definition Interest can be credited to an account more often than annually. The frequency at which interest is credited is called the compounding period.

38 Sec 2 Nominal Interest If you have a credit card, generally the interest rate will be stated as 18% interest convertible (compounded) monthly. This means that interest is compounded 12 times each year. The interest rate i to be credited each month is i = n r = =.015

39 Sec 2 Nominal Interest Problem Given an initial balance of $1000, absent of any additional charges to your account, after 6 months, what will be the account balance? 6.18 A 6 = P ( ) 6 = =

40 Sec 2 Nominal Interest Definition An interest rate that is compounded more frequently than annually is called a nominal interest rate.

41 Sec 2 Nominal Interest Problem If you have 5000 in a bank account earning 4% compounded quarterly, what will be your account balance in 10 years?

42 Sec 2 Nominal Interest P 0 = 5000 r =.04 n = 4 t = 4 10 = A 40 = =

43 Sec 2 Present Value Compound Amount Formula A t = P0 1+ r n where t is the number of number of compounding periods per year times the number of full and fractional years in the investment period. t

44 Sec 2 Present Value Problem If you want to have $10,000 for the down payment on a house in 5 years, how much should you deposit in an account today earning 8% compounded semiannually?

45 Sec 2 Present Value r =.08 n = 2 t = 2 5 = 10 A 10 =10000 P 0 =?

46 Sec 2 Present Value = P P0 = =

47 Sec 2 Present Value Present Value Formula P 0 = A 1 + t r n t where t is the number of number of compounding periods per year times the number of full and fractional years in the investment period.

48 Sec 2 Inflation Problem You have $8,000 for a deposit on a house. Your plan is to purchase a house in 5 year. If your deposit will earn 5% compounded monthly, how much will you have to purchase your house?

49 Sec 2 Inflation P 0 = 8000 r =.05 n =12 t = 12 5 = A 60 = = $10,267 60

50 Sec 2 Inflation Problem If you need a 10% deposit to buy your home, what is the maximum value of the house you can afford?. 1 x = x =102670

51 Sec 2 Inflation Problem If the cost of housing continues to increase at a rate of 4%, what is the present value of the home you will be able to afford 5 years from now?

52 Sec 2 Inflation r =.04 n =1 t = 1 5 = 5 A 5 = P = 0 ( 1+.04) 5 = $84,387

53 Sec 2 Effective Interest Rate It is important to be able to compare interest rates. For instance, let s compare how much we will have at the end of the year if we invest $1 at 6% interest, but the interest is compound at various frequencies.

54 Sec 2 Effective Interest Rate Frequency Annual Rate = = = =

55 Sec 2 Effective Interest Rate Definition The equivalent annual interest rate is called the effective rate of interest.

56 Sec 2 Assignment Pages , 5, 17, 21, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 69, 73, 77, 81, 85, 89