Copyright © 2012 Pearson Education, Inc. All rights reserved 5.2(Day2) Future Value of an Annuity

5 - 2 Vocabulary  Annuity: A sequence of equal payments made at equal periods of time.  Ordinary Annuity: If the payments are made at the end of the time period, and if the frequency of payments is the same as the frequency of compounding, the annuity is called an ordinary annuity. © 2012 Pearson Education, Inc.. All rights reserved.

5 - 3 Vocabulary  The future value of the annuity is the final sum on deposit defined as the sum of the compound amounts of all the payments, compounded to the end of the term. © 2012 Pearson Education, Inc.. All rights reserved.

5 - 4 Future Value of an Ordinary Annuity © 2012 Pearson Education, Inc.. All rights reserved.

5 - 5 Example 1: Ordinary Annuity  Steven is an athlete who believes that his playing carrier will last 7 years. To prepare for his future, she deposits $ 22, 000 at the end of each year for 7 years in an account paying 6% compounded annually. (1) How much will he have on deposit after 7 years? (2) How much of this value is from his contribution and how much is from interest? © 2012 Pearson Education, Inc.. All rights reserved.

5 - 6 Vocabulary  Sinking Funds A fund set up to receive periodic payments is called a sinking fund. The periodic payments, together with the interest earned by the payments, are designed to produce a given sum at some time in the future. © 2012 Pearson Education, Inc.. All rights reserved.

5 - 7 © 2012 Pearson Education, Inc.. All rights reserved.

5 - 8 Example 2: Sinking Fund  Nancy has decided to deposit $ 200 each month for 20 years in an account that pays interest of 7.2% compounded monthly. (a) How much will be in the account at the end of 20 years? (b) Nancy believes she needs to accumulate $ 130,000 in the 20-year period to have enough for retirement. To meet this goal, she must increase her monthly payment. What payment should she make each month? © 2012 Pearson Education, Inc.. All rights reserved.

Copyright © 2012 Pearson Education, Inc. All rights reserved 5.3 Present Value of an Annuity;Amortization

Vocabulary  Annuity: A sequence of equal payments made at equal period of time ”  The present value of Annuity is the amount that would have to be deposited in one lump sum today (at the same compound interest rate) in order to produce exactly the same balance at the end of entire loan period. © 2012 Pearson Education, Inc.. All rights reserved.

© 2012 Pearson Education, Inc.. All rights reserved.

Your Turn 1 Find the present value of an annuity of $120 at the end of each month put into an account yielding 4.8% compounded monthly for 5 years. © 2012 Pearson Education, Inc.. All rights reserved.

Your Turn 2 A car costs $19,000. After a down payment of $2000, the balance will be paid off in 48 equal monthly payments with interest of 5.4% per year on the unpaid balance. Find the amount of each payment. Continued © 2012 Pearson Education, Inc.. All rights reserved.

Vocabulary  Amortization: A loan is amortized if both the principal and interest are paid by a sequence of equal period payments.  In other words, amortization is to pay off a debt with a fixed repayment schedule in regular installments over a period of time.fixed repayment schedule © 2012 Pearson Education, Inc.. All rights reserved.

© 2012 Pearson Education, Inc.. All rights reserved.

Example: Early Payment  Amy borrow $1000 for 1 year at 12% annual compounded monthly. (1)What is her monthly payment? (2) After making three payments, she decides to pay off the remaining balance all at once. How much must she pay? © 2012 Pearson Education, Inc.. All rights reserved.

Determine the exact amount Amy owes after three monthly payments. © 2012 Pearson Education, Inc.. All rights reserved.

Copyright © 2012 Pearson Education, Inc. All rights reserved Chapter 5 Review Extended Application: Time, Money and Polynomials

© 2012 Pearson Education, Inc.. All rights reserved. Figure 15

Figure 16 © 2012 Pearson Education, Inc.. All rights reserved.