Amortization and Sinking Fund Chapter 7. Sir Migo Mendoza

Transcription

1 Amortization and Sinking Fund Chapter 7 Sir Migo Mendoza

2 Basic Concepts in Amortization Lesson 7.1 Sir Migo Mendoza

3 Do you know? One of the most important and most common applications of annuities in business is the repayment of interestbearing debts: 1. Amortization; and 2. Sinking Funds.

4 Amortization It is a financial arrangement whereby a lump-sum is incurred at compound interest now, such as loan, and is liquidated or paid off or by a series of equal periodic payment for a specified amount of time (e.g. monthly, quarterly, semiannually, annually, etc.)

5 Amortization of Loan It is the repayment of a loan by periodic payments, with the possible exception of the last payment, are equal in size.

6 Note: When the debt is paid on a series of equal payments, pay the interest outstanding at the time the payments are made and also repay a part of the principal. As the principal gradually reduced by periodic payments, the interest of the unpaid balance decreases.

7 Amortization Period It is the length of time over which a loan is scheduled to be fully repaid.

8 Amortization Schedule It is a list of several periods of payments showing the principal and the interest parts of those payments and the outstanding balance (or principal) after each payment is made.

9 Note: After the two parties (lender and borrower) agreed on the amount of a loan, the rate of interest, and the repayment frequency, after of which the amortization schedule will be established.

10 Note: Majority of the financing institutions provide the borrower with an amortization schedule. The data on the amortization schedule are important to the borrower for two reasons:

11 First: the borrower needs to know the total interest paid; and

12 Second: the borrower needs the data if he/she is planning paying off the loan early.

13 Computing the Present Value of an Amortization Lesson 7.2 Sir Migo Mendoza

14 Introduction: With amortization, the original amount of the loan (present value or obligation) is known; therefore we use the present value formula for ordinary simple annuity.

15 Formula for Computing the Present Value of an Amortization:

16 Note: In our final computation, we will include three significant decimal digits to generate a more accurate result. Also, we will apply only the Ordinary Simple Annuity.

17 Example 7.1 A loan of 7 quarterly payments of P8, is to be made, to pay of a loan at 10% compounded quarterly. Find the value of the loan and construct an amortization schedule.

18 Answer: The present value of the loan is P52,

19 Question: The example requested us to construct an amortization schedule, how can we do that?

20 Steps in Creating an Amortization Schedule Lesson 7.2 Sir Migo Mendoza

21 Step 1: Build a strong familiarization of the following variables will be used in amortization schedule:

22 OPBI Outstanding Principal at Beginning of Interval

23 POP Previous Outstanding Principal

24 PRP Previous Repayment of Principal

25 IDEI Interest Due at the End of Interval

26 RII Rate of Interest per Interval

27 TPEI Total Payment of Principal at the End of Interval

28 RPEI Repayment of Principal at the End of Interval

29 Step 2: Construct an Amortization Schedule Table with heading such as:

30 Columns Column 1: Period Column 2: Outstanding Principal at the Beginning of Interval (OPBI) Column 3: Interest Due at the End of Interval (IDEI) Column 4: Total Payment at the End of the Interval (TPEI) Column 5: For Repayment of Principal at the End of Interval (RPEI)

31 The Amortization Schedule Table

32 Step 3: Determine the value of OPBI, IDEI, TPEI and RPEI for the first period using the following formula:

33 Formula for Computing the Outstanding Principal at the Beginning of Interval (OPBI):

34 Formula for Computing the Interest Due at the End of Interval (IDEI):

35 Formula for Computing the Total Payment at the End of Interval (TPEI):

36 Formula for Computing the Repayment of Principal at the End of Interval (RPEI):

37 The Amortization Schedule Table

38 Step 4: Compute for the OPBI, IDEI, TPEI, and RPEI for the next period up to the nth period.

39 The Amortization Schedule Table

40 The Amortization Schedule Table

41 Computing the Periodic Payment of an Amortization Lesson 7.3 Sir Migo Mendoza

42 Introduction Here, the formula for finding the periodic payment for ordinary simple annuity given the present value will be used to determine the periodic payment of an ordinary simple annuity in amortization problem.

43 Formula Computing the Periodic Payment of an Amortization

44 Example 7.2 A Php30, loan at 15% compounded semiannually is to be amortized every 6 months for 3 years. Find the quarterly payment and construct an amortization schedule.

45 Answer: The amortization payment is P6,

46 The Amortization Schedule Table

47 The Amortization Schedule Table

48 Basic Concepts in Sinking Fund Lesson 7.4 Sir Migo Mendoza

49 Introduction: Annuities can also be applied in business when a sum of money will be needed at some future date, a good practice is to build up systematically a fund that will equal the amount of money desired at the time it is needed.

50 Sinking Fund A sinking fund is an interestearning account into which periodic payments are made for the purpose of accumulating a specific amount of money by a certain date or for the purpose of saving for a future obligation.

51 Note: The accumulated funds are typically used to acquire an asset requiring a substantial capital expenditure, or to retire the principal amount of a debt.

52 Note: A sinking fund is also a systematic means for a business or other organization to accumulate funds for future project, or planned capital expenditure like the replacement of equipment, expansion of production facilities, or an acquisition.

53 Note: The easiest sinking fund arrangement requires equal periodic payments of a size computed to accumulate the required amount of money by the target date.

54 Note: The sinking fund is typically set up so that the interval between contributions equals the compounding interval. The periodic payments represent an ordinary simple annuity.

55 Computing the Future Value of a Sinking Fund Lesson 7.4 Sir Migo Mendoza

56 Introduction We will determine the future value of a sinking fund using the formula for computing the future value of ordinary simple annuity.

57 Note:

58 Note: In our final computation, we will include three significant decimal digits to generate a more accurate result. Also, we will apply only the Ordinary Simple Annuity.

59 Example 7.3 Ms. Maia Dereguito invests Php5, every 3 months at 16% compounded quarterly to accumulate a fund. How much must the fund be in 1 year and 3 months, just after the deposit due then is made? Construct a sinking fund schedule.

60 Answer: The fund will accumulate to Php29,

61 Question: In our example we are requested to construct a sinking fund schedule, how can we construct that?

62 Steps in Constructing a Sinking Fund Schedule Lesson 7.4 Sir Migo Mendoza

63 Step 1: Build a strong familiarization of the following variables will be used in sinking fund schedule:

64 FBI Fund at the Beginning of Interval

65 PBFEI Previous Balance in Fund at the End of Interval

66 IRFEI Interest Received of Fund at the End of Interval

67 RII Rate of Interest per Interval

68 PFEI Payment of Fund at the End of Interval

69 FEI Fund at the End of Interval

70 Step 2: Construct a Sinking Fund Schedule Table with the following column headings:

71 Columns Column 1: Payment Interval Column 2: In Fund at the Beginning of Interval (FBI) Column 3: Interest Received of Fund at the End of Interval (IRFEI) Column 4: Payment to Fund at the End of Interval (PFEI) Column 5: In Fund at the End of the Interval (FEI)

72 The Sinking Fund Schedule Table

73 Step 3: Determine the value of FBI, IRFEI, PFEI, and FEI for the first period using the following formula:

74 Formula for Computing the Fund at the Beginning of Interval (FBI):

75 Formula for Computing the Interest Received of Fund at the End of Interval (IRFEI):

76 Formula for Computing the Payment to Fund at the End of Interval (PFEI):

77 Formula for Computing the In Fund at the End of Interval (FEI):

78 The Sinking Fund Schedule Table

79 Step 4: Compute for the FBI, IRFEI, PFEI, and FEI for the next period up to the nth payment interval.

80 The Sinking Fund Schedule Table

81 The Sinking Fund Schedule Table

82 Computing the Periodic Payment of a Sinking Fund Lesson 7.5 Sir Migo Mendoza

83 Introduction Here, to calculate the value of the periodic payment of a sinking fund we will do the same method for finding the value of periodic payment of an ordinary simple annuity.

84 Formula Computing the Periodic Payment of a Sinking Fund

85 Example 7.4 The sum of Php14, will be needed at the end of 1 1/2 years. If money can be invested at 12% quarterly, find the periodic payment and construct a sinking fund schedule.

86 Answer: The periodic payment is P2,

87 The Sinking Fund Schedule Table

88 The Sinking Fund Schedule Table

89 Let s Practice Lesson 7.5 Sir Migo Mendoza

90 Direction: Solve the following. 1. Doctor Mike borrows a certain sum that bears interest at 14% compounded quarterly for 2 years. He agrees to pay Php at the end of every 3 months to discharge his debt. Find the original debt and construct the amortization schedule. 2. Jeron Alvin Teng deposits Php5, in a commercial bank every month, in order to accumulate at the end of 6 months on educational fund for his eldest brother Jeric Allen Teng. What is the final amount in the fund if it is invested at 12% compounded monthly? Construct a sinking fund schedule.