1. Annuities Student Handout

2. Annuities Annuity (Definition)
An annuity is series of regular payments (or withdrawals) of the same amount each time.
Two basic types of annuity problems: 1. 2.

3. Calculating Annuities using a timeline
Ex #1 – Find the future value of $500 deposited at the end of each year for 4 years at an annual interest rate of 8% compounded annually.
A= R = i = n =
Now
500
500
500
500
Therefore, the annuity will be worth $

4. Using the Formula

5. Calculating Annuities using technology
Ex #1 – Find the future value of $500 deposited at the end of each year for 4 years at an annual interest rate of 8% compounded annually.
Payment =
Annual Rate% =
Periods =
Compounding =
Then click on FV
Futute Value is $

6. Calculating Annuities using technology
Ex #2 – Find the present value of a series of regular $500 withdrawals from an investment account earning 8%/a compounded monthly. Assume you are withdrawing $500 per year for 4 years at the end of the year.
Payment =
Annual Rate% =
Periods =
Compounding =
Then click on PV
Present Value is $

7. Using a Timeline
Ex #2 – Find the present value of a series of regular $500 withdrawals from an investment account earning 8%/a compounded monthly. Assume you are withdrawing $500 per year for 4 years at the end of the year.

8. Using the Graphing Calculator App
N – total number of payments
I% - annual interest rate (as a percent)
PV – present value
PMT – payment amount
FV – future value
P/Y – payments per year
C/Y – compounding periods per year
PMT : BEGIN – indicates if the payment is at the end or the beginning of the payment cycle
Entered as negative if money is paid out
END
Steps to solve:
1. Enter all the information you are given, leaving the unknown value blank.
2. Scroll back to the unknown value, highlight it and hit
Alpha
Enter

9. Technology Examples
Ex #1 – Calculate your car payments if you have borrowed $10,000 for 4 years, with an interest rate of 4.8%/a compounded monthly and your payments are monthly at the end of the month.

10. Technology Examples
Ex #2 – You want to retire with $ Find the amount you must deposit monthly for 35 years if your retirement investment fund (RIF) earns 6.4%/a compounded monthly. Assume you are depositing your money at the end of the month.

11. Homework / Practice Solve the following problems using a timeline.
Find the future value of $400 deposited at the beginning of each year for 4 years at an annual interest rate of 12% compounded monthly.
Find the present value of a series of regular $1000 withdrawals from an investment account earning 5%/a compounded monthly. Assume you are withdrawing $1000 per year for 4 years at the end of the year.
Answers: 1. $ $
Practice using formulas with textbook questions.