first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest.

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1 ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular Deposits using chart and equation 1

2 Terms to be familiar with: Annuity Interest Compound Interest Amount of an Annuity Ammortization Present Value Future Value Compounding Period 2

3 Work with a partner to investigate the following scenario. Suppose you are able to deposit $1000 at the end of each year into an investment account. You do this for 5 years. The account earns you 6% compounded annually. How much will you have saved at the end of 5 years? Year Starting Balance Interest Earned 6% Deposit Ending Balance 1 $ $1000 $ $1000 $60.00 $1000 $ Why does the interest earned increase each year? What is an advantage and disadvantage of using a table to determine the savings after 5 years? 3

4 4

5 ORDINARY SIMPLE ANNUITY: equal payments made at regular intervals paid at the end of each compounding period Amount of an Annuity = the sum of the regular payments/deposits PLUS interest TERMS TO KNOW: A = P ( 1 + i) n ANNUALLY SEMI-ANNUALLY QUARTERLY MONTHLY WEEKLY BI-WEEKLY To Calculate "i" annual interest rate as a decimal (not %) # of compounding periods in 1 year 4.5% compounded semi annually 5 1/4% compounded monthly To determine "n" as it would appear in the C. I. Formula... "n" = It is the TOTAL number of times interest will be compounded over a specified period of time ie. length of a loan every month (monthly) for 2 years weekly for 18 months 5

6 EXAMPLE: using a table Suppose $450 is deposited at the end of each quarter for 1.5 years, in an investment account that earns 10% per year, compounded quarterly. a) What is the amount of the annuity? b) How much interest does the annuity earn? The annual interest rate is 10%, so the QUARTERLY rate is... How many QUARTERS are there in 1.5 years? Quarter Starting Balance Interest Earned (2.5%) Deposit Ending Balance $ $ $ $11.25 $ $ $ $ $ $ Total The AMOUNT of the annuity is... The INTEREST earned is... USING THE EQUATION: A = the amount in dollars R = the regular payment in dollars i = the interest rate per compounding period n = the number of compounding periods Using the example above, determine what you need in order to solve the same problem, using the equation. Determine the value of all the variables 6

7 RESTRICTIONS ON THE FORMULA: payment interval is the SAME as the COMPOUNDING PERIOD payment is made at the END of each compounding period the first payment is made at the end of the first compounding period USING TVM SOLVER on graphing calculator: set the calc to 2 decimal places Open TVM solver --APPS > FINANCE > TVM SOLVER The Variables represent the following quantities: N total number of payments I% Annual interest rate PV Principal or present value PMT Regular payments FV Amount or Future Value P/Y Number of payments per year C/Y Number of Compounding periods per year PMT: Indicates whether payments are made at the beginning or end of the payment period the calculator displays either POSITIVE or NEGATIVE values for PV, PMT and FV ---Negative means that money is paid OUT in annuity calculations, only one of the amount (FV) or present value (PV) is used. Enter 0 for the variable not used 7

8 EXAMPLE: using TVM Solver. Suppose $450 is deposited at the end of each quarter for 1.5 years, in an investment account that earns 10% per year, compounded quarterly. a) What is the amount of the annuity? b) How much interest does the annuity earn? What values do you enter into the Calculator? N I% PV PMT FV P/Y C/Y PMT: to solve the Amount move CURSOR to FV press ALPHA> ENTER 8

9 PRACTICE: SIMPLE ANNUITIES, AMOUNT of an ANNUITY 9

10 10

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