ANNUITIES INTRO.notebook
ANNUITIES INTRO.notebook
December 15, 2011
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
ANNUITIES INTRO.notebook
December 15, 2011
Terms to be familiar with:
Annuity
Interest
Compound Interest
Amount of an Annuity
Ammortization
Present Value
Future Value
Compounding Period
2
ANNUITIES INTRO.notebook
December 15, 2011
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
$0.00
0.00
$1000
$1000
2
$1000
$60.00
$1000
$2060.00
3 4 5
• 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
ANNUITIES INTRO.notebook
December 15, 2011
4
ANNUITIES INTRO.notebook
December 15, 2011
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 semiannually
51/4% 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
ANNUITIES INTRO.notebook
December 15, 2011
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
1
0.00
0.00
$450.00
$450.00
2
$450.00
$11.25
$450.00
$911.25
3
$450.00
4
$450.00
5
$450.00
6
$450.00 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
ANNUITIES INTRO.notebook
December 15, 2011
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 I% PV PMT FV P/Y C/Y PMT:
total number of payments Annual interest rate Principal or present value Regular payments Amount or Future Value Number of payments per year Number of Compounding periods per year 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
ANNUITIES INTRO.notebook
December 15, 2011
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? PV I% N FV
P/Y
C/Y
PMT PMT:
to solve the Amount move CURSOR to FV press ALPHA> ENTER
8
ANNUITIES INTRO.notebook
December 15, 2011
PRACTICE: SIMPLE ANNUITIES, AMOUNT of an ANNUITY
9
ANNUITIES INTRO.notebook
December 15, 2011
10
December 15, 2011
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
ANNUITIES INTRO.notebook
December 15, 2011
Terms to be familiar with:
Annuity
Interest
Compound Interest
Amount of an Annuity
Ammortization
Present Value
Future Value
Compounding Period
2
ANNUITIES INTRO.notebook
December 15, 2011
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
$0.00
0.00
$1000
$1000
2
$1000
$60.00
$1000
$2060.00
3 4 5
• 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
ANNUITIES INTRO.notebook
December 15, 2011
4
ANNUITIES INTRO.notebook
December 15, 2011
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 semiannually
51/4% 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
ANNUITIES INTRO.notebook
December 15, 2011
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
1
0.00
0.00
$450.00
$450.00
2
$450.00
$11.25
$450.00
$911.25
3
$450.00
4
$450.00
5
$450.00
6
$450.00 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
ANNUITIES INTRO.notebook
December 15, 2011
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 I% PV PMT FV P/Y C/Y PMT:
total number of payments Annual interest rate Principal or present value Regular payments Amount or Future Value Number of payments per year Number of Compounding periods per year 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
ANNUITIES INTRO.notebook
December 15, 2011
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? PV I% N FV
P/Y
C/Y
PMT PMT:
to solve the Amount move CURSOR to FV press ALPHA> ENTER
8
ANNUITIES INTRO.notebook
December 15, 2011
PRACTICE: SIMPLE ANNUITIES, AMOUNT of an ANNUITY
9
ANNUITIES INTRO.notebook
December 15, 2011
10
