LESSON OF SIMPLE ANNUITY

1. BASIC BUSINESS MATHEMATICS

2. MATH PRAYER
Lord, teach us to number our days
and graph them according to your
ways. Trusting you to guide us
everyday. Subtract the points that you
don’t want from me but add the values
that I possess accordingly. Divide the
dividends hypothetically, so that I can
multiply them systematically.
Amen.

3. Text content
ENTRY CARD!
Answer each of the following:
1. ₱50,000 is invested for 5 years at 8% compounded quarterly.
Give the value of each variable in the formula
𝑨 = 𝑷(𝟏 + 𝒊)𝒏
𝐰𝐡𝐞𝐫𝐞 𝒊 =
𝒓
𝒎
𝐚𝐧𝐝 𝒏 = 𝒎𝒕
a). P =
b). r =
c). i =
d). n =

4. Illustrate Simple and General Annuities
According to
payment
interval and
interest period.
Simple Annuity - an annuity
where the payment interval
is the same as the interest
period.
General Annuity - an annuity
where the payment interval
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.
Annuity Due - a type of
annuity in which the
payments are made at
beginning of each payment
interval.
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)

5. Text content
DEFINITION OF TERMS
Term of an Annuity (t) - time between the first payment
interval and last payment interval.
Regular or Periodic Payment (R) - the amount of each
payment.
Amount (Future Value) of an Annuity (F) - sum of future
values of all the payments to be made during the entire
term of the annuity.
Present Value of an Annuity (P) - present value of all
payments to be made during the entire term of the annuity.

6. FORMULA
Future Value of Simple
Ordinary Annuity, F
Present Value of Simple
Ordinary Annuity, P
Periodic Payment R of an
Annuity
𝑭 = 𝑹
(𝟏 + 𝒊)𝒏
−𝟏
𝒊
𝑷 = 𝑹
𝟏 − (𝟏 + 𝒊)−𝒏
𝒊
𝑹 =
𝑭
(𝟏 + 𝒊)𝒏−𝟏
𝒊
𝑹 =
𝑷
𝟏 − (𝟏 + 𝒊)−𝒏
𝒊
𝒊 =
𝒓
𝒎
, 𝒏 = 𝒎𝒕
where; R - is the regular payment
i - is the interest rate per period
n - is the number of payments
r - is the nominal rate
m - is the number of conversion periods

7. EXAMPLE
1. Determine if the given situations represent simple
annuity or general annuity.
a) Payments are made at the end of each month for a
loan that charges 1.05% interest compounded
quarterly.
b) A deposit of ₱5,000.00 was made at the end of three
months to an account that earns 5.6% interest
compounded quarterly.

8. EXAMPLE
1. Determine if the given situations represent simple
annuity or general annuity.
a) Payments are made at the end of each month for a
loan that charges 1.05% interest compounded
quarterly.
b) A deposit of ₱5,5000.00 was made at the end of
three months to an account that earns 5.6% interest
compounded quarterly.
GENERAL ANNUITY

9. EXAMPLE
1. Determine if the given situations represent simple
annuity or general annuity.
a) Payments are made at the end of each month for a
loan that charges 1.05% interest compounded
quarterly.
b) A deposit of ₱5,5000.00 was made at the end of
three months to an account that earns 5.6% interest
compounded quarterly.
GENERAL ANNUITY
SIMPLE ANNUITY

10. EXAMPLE
2.Determine whether the situation describes an
ordinary annuity or an annuity due.
a) Jun’s monthly mortgage payment is ₱35,148.05 at
the end of each month.
b) The rent of apartment is ₱7,000.00 and due at the
beginning of each month.

11. EXAMPLE
2.Determine whether the situation describes an
ordinary annuity or an annuity due.
a) Jun’s monthly mortgage payment is ₱35,148.05 at
the end of each month.
b) The rent of apartment is ₱7,000.00 and due at the
beginning of each month.
ORDINARY ANNUITY

12. EXAMPLE
2.Determine whether the situation describes an
ordinary annuity or an annuity due.
a) Jun’s monthly mortgage payment is ₱35,148.05 at
the end of each month.
b) The rent of apartment is ₱7,000.00 and due at the
beginning of each month.
ORDINARY ANNUITY
ANNUITY DUE

13. EXAMPLE
Rose works very hard because she want
to have enough money in her retirement
account when she reaches the age 60. She
wants to withdraw ₱36,000.00 every 3
months for 20 years starting 3 months after
she retires. How much must Rose deposit
at retirement at 12% per year compounded
quarterly for the annuity?

14. EXAMPLE
Given: Find: Present Value
R = ₱36,000 𝑷 = 𝑹
𝟏−(𝟏+𝒊)−𝒏
𝒊
r = 0.12 𝑷 = 𝟑𝟔, 𝟎𝟎𝟎
𝟏−(𝟏+𝟎.𝟎𝟑)−𝟖𝟎
𝟎.𝟎𝟑
t = 20 years
m = 4 𝑷 = ₱𝟏, 𝟎𝟖𝟕, 𝟐𝟐𝟕. 𝟒𝟖
n = mt = (20)(4) = 80
i = r/m = 0.12/4 = 0.03

15. EXAMPLE
Given: Find: Present Value
R = ₱36,000 𝑷 = 𝑹
𝟏−(𝟏+𝒊)−𝒏
𝒊
r = 0.12 𝑷 = 𝟑𝟔, 𝟎𝟎𝟎
𝟏−(𝟏+𝟎.𝟎𝟑)−𝟖𝟎
𝟎.𝟎𝟑
t = 20 years
m = 4 𝑷 = ₱𝟏, 𝟎𝟖𝟕, 𝟐𝟐𝟕. 𝟒𝟖
n = mt = (20)(4) = 80
i = r/m = 0.12/4 = 0.03

16. EXAMPLE
Paolo borrowed ₱100,000.00. He agrees to pay the
principal plus the interest by paying an equal amount
of money each year for 3 years. What should be his
annual payment if interest is 8% compounded
annually?

17. EXAMPLE
Paolo borrowed ₱100,000.00. He agrees to pay the
principal pllus the interest by paying an equal amount
of money ecah year for 3 years. What should be his
annual payment if interest is 8% compounded
annually?
Given:
P = ₱100,000 n = mt = (1)(3) = 3
r = 0.08 i = r/m = 0.08/1 = 0.08
t = 3 years
m = 1

18. EXAMPLE
Find: Periodic Payment, R
𝑹 =
𝑷
𝟏 − (𝟏 + 𝒊)−𝒏
𝒊
𝑹 =
𝟏𝟎𝟎, 𝟎𝟎𝟎
𝟏 − (𝟏 + 𝟎. 𝟎𝟖)−𝟑
𝟎. 𝟎𝟖
𝑹 = ₱𝟑𝟖, 𝟖𝟎𝟑. 𝟑𝟓

19. EXAMPLE
Find: Periodic Payment, R
𝑹 =
𝑷
𝟏 − (𝟏 + 𝒊)−𝒏
𝒊
𝑹 =
𝟏𝟎𝟎, 𝟎𝟎𝟎
𝟏 − (𝟏 + 𝟎. 𝟎𝟖)−𝟑
𝟎. 𝟎𝟖
𝑹 = ₱𝟑𝟖, 𝟖𝟎𝟑. 𝟑𝟓

20. EXAMPLE
Mr. Ribaya would like to save
₱500,000 for his son’s college
education. How much should he
deposit in a savings account every 6
months for 12 years if interest is 1%
compounded semi-annually?

21. FORMULA SUMMARY
Future Value of Simple
Ordinary Annuity, F
Present Value of Simple
Ordinary Annuity, P
Periodic Payment R of an
Annuity
𝑭 = 𝑹
(𝟏 + 𝒊)𝒏
−𝟏
𝒊
𝑷 = 𝑹
𝟏 − (𝟏 + 𝒊)−𝒏
𝒊
𝑹 =
𝑭
(𝟏 + 𝒊)𝒏−𝟏
𝒊
𝑹 =
𝑷
𝟏 − (𝟏 + 𝒊)−𝒏
𝒊
𝒊 =
𝒓
𝒎
, 𝒏 = 𝒎𝒕
where; R - is the regular payment
i - is the interest rate per period
n - is the number of payments
r - is the nominal rate
m - is the number of conversion periods

22. QUESTIONS
1. What is the formula for finding the Future Value of
Simple Ordinary Annuity (F)?
2. What is the formula for finding the Present Value of
Simple Ordinary annuity (P)?
3. What are the formulas for finding the Periodic
Payment (R) of an annuity?

23. SHORT TEST
Directions: Copy and answer the following questions.
Write your answer on a 1 whole sheet of paper. (Show
your solutions).
1. Suppose Mrs. Remoto would like to save ₱3,000
every month in a fund that gives 9% compounded
monthly. How much is the amount or the future value
of her savings after 6 months?
2. In order to save for her high school graduation.
Marie decided to save ₱200 at the end of each month.
If the bank pays 0.25% compounded monthly, how
much will her money be at the end of 6 years?

24. THANKS