The document discusses simple and general annuities. It defines an annuity as a sequence of payments made at regular intervals, such as monthly pension payments or installment loans. A simple annuity has payment and compounding intervals that are equal, while a general annuity has unequal payment and compounding intervals. Examples of simple annuities include car loans with monthly payments and monthly compounding interest. Mortgages are an example of a general annuity, with monthly payments but semi-annual compounding interest. The document also provides formulas for calculating the present and future values of simple and general annuities.

1. C
SIMPLE AND GENERAL
ANNUITY

2. REMEMBER:
Kaya mo yan baby, wag kang tamarin mag-aral lalo na
sa Math. Wag mong iisipin na mahirap ganun or dimo
maintindihan ha
I LOVE YOU SO MUCH MWAAAA, fighting my love
(look ka sa notes below)

3. 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.

4. 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)

5. •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).

6. DIFFERENTIATE
SIMPLE ANNUITY FROM
GENERAL ANNUITY

8. 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.

9. SIMPLE ANNUITY GENERAL ANNUITY
I. 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.
II. A college educational plan earns 4%
compounded quarterly and payments are made
quarterly.
1. Life insurance contribution paid monthly while
the interests is compounded quarterly
2. 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

10. •BABY MAG SEARCH KA NG MGA
POSSIBLE REAL LIFE PROBLEMS
INVOLVING SIMPLE AND GENERAL
ANNUITY AND EXAMPLE yung parang
ibinigay din ni sir na nilagay ko

11. FORMULAS

12. • Baby di ako sure sa mga formulas gagi, ilang beses ko ng
chineck pero naguguluhan pa din ako kasi iba iba kasi
yung ginagamit ng iba na nassearch ko. Tapos iba din
yung nasa notebook ko na naisulat ko na sinabi noon ni
sir. E baka gisahin kayo ng mga kaklase natin lalo na si
Emman, baka masapak ko pa siya bigla kapag kaya I
double check mo nalang. I love you mwa mwa fighting!

13. SIMPLE ANNUITY
PRESENT VALUE FUTURE VALUE
SIMPLE ANNUITY
𝑃 = 𝑅
1 − (1 + r/n)−𝑛𝑡
𝑟
𝑛
Where
P - Present Value
R – Regular payment
r - interest rate per period
t - number of years
where
𝑟
𝑛
- annual rate
n - number of conversion period in a
year
−𝑛𝑡 - total number of conversion
𝐹 = 𝑅
(1 + r/n)𝑛𝑡
−1
𝑟
𝑛
Where
F - Future Value or Amount
R – Regular Payment
r - interest rate per period
t - number of years
where
𝑟
𝑛
- annual rate
n - number of conversion period in a year
- total number of conversion

14. GENERAL ANNUITY
PRESENT VALUE FUTURE VALUE
GENERAL
ANNUITY 𝑖 = (1 +
𝑟
𝑚2
)
𝑚2
𝑚1
−1
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
𝑃 = 𝑅
1 − (1 + i)−𝑛
𝑖
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
𝐹 = 𝑅
(1 + i)𝑛
−1
𝑖
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