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Lecture Financial institutions, instruments and markets (7e): Chapter 8 – Viney, Phillips

Chapter 8 - Mathematics of finance: An introduction to basic concepts and calculations. After studying this chapter you will be able to understand and carry out simple interest calculations to determine. Understand and carry out compound interest calculations to determine. | Chapter 8 Mathematics of finance: An introduction to basic concepts and calculations Learning objectives Understand and carry out simple interest calculations to determine: accumulated amount present value yields holding period yield Understand and carry out compound interest calculations to determine: accumulated amount (future value) present value present value of an annuity accumulated value of an annuity (future value) effective rate of interest Chapter organisation 8.1 Simple interest Simple interest accumulation Present value Yields Holding period yield 8.2 Compound interest Compound interest accumulation (future value) Present value Present value of an annuity Accumulated value of an annuity (future value) Effective rates of interest 8.3 Summary 8.1 Simple interest Introduction Focus is on the mathematical techniques for calculating the cost of borrowing and the return earned on an investment Table 8.1 defines the symbols of various formulae Although symbols vary between textbooks, formulae are consistent (cont.) 8.1 Simple interest (cont.) (cont.) 8.1 Simple interest (cont.) Simple interest is interest paid on the original principal amount borrowed or invested The principal is the initial, or outstanding, amount borrowed or invested With simple interest, interest is not paid on previous interest The amount of interest paid on debt, or earned on a deposit is: where: A is the principal d is the duration of the loan, expressed as the number of interest payment periods (usually one year) i is the interest rate, expressed as a decimal (cont.) Simple interest accumulation Example 1: If $10 000 is borrowed for one year, and simple interest of 8% per annum is charged, the total amount of interest paid on the loan would be: I = A d/365 i = 10 000 365/365 0.08 = $800 Example 2: Had the same loan been for two years the total amount of interest paid would be: I = 10 000 730/365 0.08 = $1600 (cont.) Simple interest accumulation . | Chapter 8 Mathematics of finance: An introduction to basic concepts and calculations Learning objectives Understand and carry out simple interest calculations to determine: accumulated amount present value yields holding period yield Understand and carry out compound interest calculations to determine: accumulated amount (future value) present value present value of an annuity accumulated value of an annuity (future value) effective rate of interest Chapter organisation 8.1 Simple interest Simple interest accumulation Present value Yields Holding period yield 8.2 Compound interest Compound interest accumulation (future value) Present value Present value of an annuity Accumulated value of an annuity (future value) Effective rates of interest 8.3 Summary 8.1 Simple interest Introduction Focus is on the mathematical techniques for calculating the cost of borrowing and the return earned on an investment Table 8.1 defines the symbols of various formulae Although symbols vary .