Simple-and-Generadgrhhhhhhhhhhhnnuity.pptx

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1. A sum of ₱8,000 grows to ₱9,414.32 in 3 years, with interest compounded quarterly. What is the interest rate?

2. A sum of ₱8,000 grows to ₱9,414.32 in 3 years, with interest compounded quarterly. What is the interest rate?

3. An initial investment of ₱10,000 grows to ₱15,000 at an interest rate of 5% per year, compounded semi-annually. How long did it take for the investment to reach this amount?

4. An initial investment of ₱10,000 grows to ₱15,000 at an interest rate of 5% per year, compounded semi-annually. How long did it take for the investment to reach this amount?

5. SIMPLE AND GENERAL ANNUITY GENERAL MATHEMATICS

6. If the payment for each period is fixed and the compound interest rate is fixed over a specified time the payment is called an annuity payment . Accounts associated with streams of annuity payments are called annuities . Annuity - a sequence of payments made at equal (fixed intervals or periods of time. The following are examples of annuities: Rental payment Monthly pensions Monthly payment for car loan Educational plan installment basis of paying a car, appliance, house and lot, tuition fee, etc.

7. Annuities may be classified in different ways, as follows: Annuities According to payment interval and interest period Simple Annuity - an annuity where the payment intervals is the same as the interest period General Annuity- an annuity where the payment intervals is not the same as the interest period According to time of payment Ordinary Annuity (or Annuity Immediate) - a type of annuity in which the payments are made at the end of each payment interval Contingent Annuity- an annuity in which the payments extend over an indefinite (or indeterminate) length of time According to duration Annuity Certain - an annuity in which payments begin and end at definite times Contingent Annuity- an annuity in which the payments extend over an indefinite (or indeterminate) length of time (ex. life insurance, pension payments)

8. Each payment in an annuity is called the periodic payment (R). The time between the successive payments dates of an annuity is called the payment interval. The time between the first payment interval and last payment interval is called term of the annuity (t). The sum of the future values of all the payments to be made during the entire term of the annuity is the future value or the amount of an annuity(F). The sum of the present values of all payments to be made during the entire term of the annuity is called the present value of n annuity (P).

9. DIFFERENTIATE SIMPLE ANNUITY FROM GENERAL ANNUITY

10. SIMPLE ANNUITY GENERAL ANNUITY An  ordinary simple annuity  has the following characteristics: Payments are made at the end of the payment intervals, and the payment and compounding frequencies are equal . The first payment occurs one interval after the beginning of the annuity. The last payment occurs on the same date as the end of the annuity. For example, most car loans are ordinary simple annuities where payments are made monthly and interest rates are compounded monthly. As well, car loans do not require the first monthly payment until the end of the first month. An ordinary general annuity has the following characteristics: Payments are made at the end of the payment intervals, and the payment and compounding frequencies are unequal . The first payment occurs one interval after the beginning of the annuity. The last payment occurs on the same date as the end of the annuity. For example, most mortgages are ordinary general annuities, where payments are made monthly and interest rates are compounded semi-annually. As with car loans, your first monthly payment is not required until one month elapses.

11. SIMPLE ANNUITY GENERAL ANNUITY Your mom decided to join their office cooperative and agreed to contribute P1000 per month beginning in January 2020 which will earn 3% compounded monthly. A college educational plan earns 4% compounded quarterly and payments are made quarterly. Life insurance contribution paid monthly while the interests is compounded quarterly Your eldest brother applied for a term life insurance. His contribution per year is P40 000 that earns 12% compounded monthly for 20 years. THESE ARE THE PROBLEMS PROVIDED BY SIR MADRID DURING OUR PREVIOUS DISCUSSION ABOUT ANNUITY

12. FORMULAS

13. SIMPLE ANNUITY PRESENT VALUE FUTURE VALUE SIMPLE ANNUITY Where P - Present Value R – Regular payment r - interest rate per period t - number of years where - annual rate n - number of conversion period in a year - total number of conversion Where F - Future Value or Amount R – Regular Payment r - interest rate per period t - number of years where - annual rate n - number of conversion period in a year - total number of conversion PRESENT VALUE FUTURE VALUE SIMPLE ANNUITY

14. GENERAL ANNUITY PRESENT VALUE FUTURE VALUE GENERAL ANNUITY where i - is the equivalent interest rate per payment interval converted from the interest rate per period. r - is the nominal rate m₁ - is the payment interval m₂ - is the length of compounding period Where R - regular payment i - is the equivalent interest rate per payment interval converted from the interest rate per period. n - total number of conversion periods Where R - regular payment i - is the equivalent interest rate per payment interval converted from the interest rate per period. n - total number of conversion periods PRESENT VALUE FUTURE VALUE GENERAL ANNUITY