1. Annuities

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:
Find the future value of a series of regular payments (eg. Savings)
Find the present value of a series of regular payments (eg car loan, retirement income funds).

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 =
500
0.08 4
Now
500
500
500
500 |
|___________________________500(1.08)3 |
|_________________500(1.08)2
|______500(1.08)1
A=500(1.08)3+500(1.08)2+500(1.08)+500
A= =
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 = 500
Annual Rate% =8 annually
Periods = 4 annually
Compounding = Annually
Then click on FV
Futute Value is $2,

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 = 500
Annual Rate% =8 annually
Periods = 4 annually
Compounding = Monthly
Then click on PV
Present Value is $

7. Challenge…Using a Timeline
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.
PV= ? R = i = n =
500
0.08/12
each year x 12
Now
500
500
500
500 |
500(1+.08/12)-24______________|
500(1+.08/12)-12_________| |
500(1+.08/12)-48__________________________| |
500(1+.08/12)-36___________________ |
A= 500(1+.08/12) (1+.08/12) (1+.08/12) (1+.08/12)-48
Therefore, the annuity will be worth $

8. Using the Graphing Calculator
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. Example 2:
How much money do you need to have saved at age 18
if you want to be able to withdraw $3000 every year from age 19 to age 21, inclusive?
Assume an interest rate of 2.5%/a compounded annually.
You may use a timeline or the annuity formula.

10. Ex #3 – 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.
Answer: $229.39

11. Ex #4 – You want to retire with $650000
Ex #4 – 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.
Answer:

12. Homework / Practice Solve the following problems using a timeline.
Find the future value of $100 deposited at the beginning of each year for 3 years at an annual interest rate of 1% compounded annually.
Find the present value of a series of regular $100 withdrawals from an investment account earning 5%/a compounded annually. Assume you are withdrawing $100 per year for 4 years at the end of the year.
Answers: 1. $ $ Practice using formulas with these questions, the textbook and the ones on the next page.

13. Practice: Try these using the formulas
3. Find the amount borrowed (present value) if you are making car loan payments of $350/month for 5 years. The interest rate is 1%/a compounded monthly.
Use the formula: Answer: $
PV= R[1-(1+i)-n]/(i)
4. If your parents deposit $100 every month into an education fund, for 18 years, how much will be in the account at the time of the last deposit. Interest rate is 3%/a compounded monthly.
Use the formula: Answer: $
A= R[(1+i)n - 1]/(i)