Statistics and Probability Annuity 02.11

Statics and Probability

1. SIMPLE ANNUITY

2. ANNUITY It is a series of equal payments made at equal intervals of time.

3. Annuity Example are regular monthly deposit, monthly rentals, SSS premium, installment payment of properties like: car, house,or home appliances, and so on.

4. Payment Interval The period of time between successive payments. It may be convenient length like one month,three months, six months and one year.

5. Illustration 1. Ana’s new year resolution is to deposit Php2,000.00 at the end of every 3–month for 4 years in a bank that pays 5% compounded monthly. How much will Ana have in her account at the end of 4 years?

6. 2 TYPES OF ANNUITY Simple Annuity General Annuity

7. Simple Annuity an annuity where the payment interval is the same as the interest period.

8. Term of an Annuity (t) The time between the first payment interval and the last payment interval.

9. Regular or Periodic Payment (R) The amount of each payment.

10. Amount (Future Value) of an annuity (F) The sum of future value of all the payments to be made during the entire term of the annuity.

11. Present Value of an annuity (P) The sum of present value of all the payments to be made during the entire term of the annuity.

12. EXAMPLE 1: Suppose Mrs. Manda would like to deposit P3,000 every month in a fund that gives 9%, compounded monthly. How much is the amount of future value of her savings after 6 months?

13. EXAMPLE 1.1: Find the future value of an ordinary annuity with a regular payment of P1,000 at 5% compounded quarterly for 3 years

14. EXAMPLE 2: To start a business, Jake wants to save a certain amount of money at the end of every month to put in an account providing 2% interest compounded monthly. His estimated start-up capital is P150,000. If he wants to start a business in 1.5 years, how much monthly deposit must he put into the account?

15. EXAMPLE 2.1: Lina wants have a fund of P130,000 and is invested at 5% interest compounded semi-annually. How much should she deposit to attain the certain amount at the end of 10 years?

16. EXAMPLE 3: Suppose Mrs. Manoda would like to deposit P3,000 every month in a fund that gives 9%, compounded monthly. How much will be the amount of present value of her savings after 6 months?

17. EXAMPLE 3.1: Find the present value of an ordinary annuity with regular quarterly payments worth P1,000 at 3% annual interest rate compounded quarterly at the end of 4 years.

18. EXAMPLE 4: A certain fund currently has P100,000 and is invested at 3% interest compounded annually. How much withdrawal can be made at the end of each year so that the fund will have zero balance at the end of 12 years?

19. EXAMPLE 4: Mendoza family has a fund of P200,000 and is invested at 7% interest compounded quarterly. How much withdrawal can be made at the end of each year so that the fund will have zero balance at the end of 20 years?