1. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. 6.4 Present Value of an Annuity; Amortization

2. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. 2 6.4 Present Value of an Annuity; Amortization The present value of an annuity is the amount that must be deposited today (at the same compounded interest rate as the annuity) to provide all the payments for the term of the annuity.

3. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. Finding the Present Value of an Annuity 3

4. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. 4 We seek a formula for the present value of an annuity ……..

5. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. 5 Theorem Present Value of an Annuity Suppose an annuity earns interest at the rate of i per payment period. If n withdrawals of $P are made at each payment period, the amount V required is Here V is called the present value of the annuity. P is the payment at the end of each period i is the interest rate per period n is the number of periods Present Value of an Annuity Suppose an annuity earns interest at the rate of i per payment period. If n withdrawals of $P are made at each payment period, the amount V required is Here V is called the present value of the annuity. P is the payment at the end of each period i is the interest rate per period n is the number of periods 6.4 Present Value of an Annuity; Amortization

6. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. Getting By in College 6

7. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. Determining the Cost of a Car 7

8. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. Lease or Purchase (a)Which alternative is preferable if the company can invest money at 5% per annum? (b)Which alternative is preferable if the company can invest money at 15% per annum? (b) 8

9. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. 9 A loan with a fixed rate of interest is said to be amortized if both principal and interest are paid by a sequence of equal payments made over equal periods of time. (The Latin word mort means “death.” Paying off a loan is regarded as “killing” it.) A loan with a fixed rate of interest is said to be amortized if both principal and interest are paid by a sequence of equal payments made over equal periods of time. (The Latin word mort means “death.” Paying off a loan is regarded as “killing” it.) 6.4 Present Value of an Annuity; Amortization

10. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. 10 Theorem Amortization The payment P required to pay off a loan of V dollars borrowed for n payment periods at a rate of interest i per payment period is Amortization The payment P required to pay off a loan of V dollars borrowed for n payment periods at a rate of interest i per payment period is 6.4 Present Value of an Annuity; Amortization

11. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. Finding the Payment for an Amortized Loan 11

12. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. Home Mortgage Payments 12

13. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. 13

14. Finite Mathematics: An Applied Approach by Michael Sullivan Copyright 2011 by John Wiley & Sons. All rights reserved. Amortization Table 14