1. INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences  2011 Pearson Education, Inc. Chapter 5 Mathematics of Finance

2.  2011 Pearson Education, Inc. To solve interest problems which require logarithms. To solve problems involving the time value of money. To solve problems with interest is compounded continuously. Chapter 5: Mathematics of Finance Chapter Objectives

3.  2011 Pearson Education, Inc. Compound Interest Present Value Interest Compounded Continuously 5.1) 5.2) 5.3) Chapter 5: Mathematics of Finance Chapter Outline

4.  2011 Pearson Education, Inc. Chapter 5: Mathematics of Finance 5.1 Compound Interest Example 1 – Compound Interest Compound amount S at the end of n interest periods at the periodic rate of r is as Suppose that $500 amounted to $588.38 in a savings account after three years. If interest was compounded semiannually, find the nominal rate of interest, compounded semiannually, that was earned by the money.

5.  2011 Pearson Education, Inc. Solution: Let r be the semiannual rate. There are 2 × 3 = 6 interest periods. The semiannual rate was 2.75%, so the nominal rate was 5.5 % compounded semiannually. Chapter 5: Mathematics of Finance 5.1 Compound Interest Example 1 – Compound Interest

6.  2011 Pearson Education, Inc. How long will it take for $600 to amount to $900 at an annual rate of 6% compounded quarterly? Solution: The periodic rate is r = 0.06/4 = 0.015. It will take. Chapter 5: Mathematics of Finance 5.1 Compound Interest Example 2 – Compound Interest

7.  2011 Pearson Education, Inc. Chapter 5: Mathematics of Finance 5.2 Present Value Example 1 – Present Value P that must be invested at r for n interest periods so that the present value, S is given by Find the present value of $1000 due after three years if the interest rate is 9% compounded monthly. Solution: S=1000, r =0.09/12, n =3(12) For interest rate,. Principle value is.

8.  2011 Pearson Education, Inc. Chapter 5: Mathematics of Finance 5.2 Present Value Example 2 – Net Present Value You can invest $20,000 in a business that guarantees you cash flows at the end of years 2, 3, and 5 as indicated in the table. Assume an interest rate of 7% compounded annually and find the net present value of the cash flows. Net Present Value YearCash Flow 2$10,000 38000 56000

9.  2011 Pearson Education, Inc. Chapter 5: Mathematics of Finance 5.2 Present Value Example 5 – Net Present Value Solution: Substracting the initial investment from the sum of the present values of the cash flows gives Since NPV <0, business venture is not profitable if one considers the time value of money. It would be better to invest the $20,000 in a bank paying 7%, since the venture is equivalent to investing only $20,000 -$457.31= $19,542.69