2. Annuity is a sequence of equal payments
made at equal intervals of time usually monthly,
quarterly, semi-annually and annually.
Some examples of annuities are:
Installment payments
Rental payments
Life insurance premiums
Weekly wages
Periodic pensions

3. Types of Annuities
Annuity certain is an annuity whose term is
fixed when the term starts and ends on definite
date.
Ex.: Monthly payment on home appliances
where payments starts on a specified date and
continue regularly until the last payment is
made.
Contingent Annuity is an annuity whose term
depends upon some uncertain events.
Ex.: Life insurance premiums and pensions

4. Classification of Annuities
Ordinary annuity is an annuity whose payments
are made at the end of each payment interval
Ex.: An annuity of P 400 payable every end of the
month for 7 years at 7% compounded monthly.
Annuity due is an annuity whose payment are
made at the beginning of each payment interval.
Ex.: An investment of P 2,000 is made at the
beginning of each month for 5 years at 9% compounded
quarterly.

5. Deferred annuity is an annuity whose first
payment is to start at some future date
Ex.: An annuity of P 500 every 3 months is to be
paid for 9 years if first payment is made at the end of 2
years where r = 8%.

6. Definition of Terms
Payment Interval is the time between consecutive
payments of annuity.
Periodic Payment (R) is the amount paid during
each installment payment period.
𝑅 =
𝑆𝑖
(1+𝑖) 𝑛 −1
or 𝑅 =
𝐴𝑖
1− (1+𝑖 )−𝑛

7. Term of annuity (t) is the time from the
beginning of the first payment interval to the end of
the last payment interval.
The total number of conversion periods in the
term of annuity is given by 𝑛 = 𝑡𝑚.
Amount of an Annuity (S) is the sum of the
values of all the periodic payments at the end of the
term.
𝑆 = 𝑅
(1 + 𝑖) 𝑛
−1
𝑖

8. Present Value of an Annuity (A) is the sum
of present values of all the payments at the
beginning of the term.
𝐴 = 𝑅
1 − (1 + 𝑖)−𝑛
𝑖
To find the Cash Equivalent (CE) of an item
bought with a down payment and the balance is
paid on equal installments for over a period of
time, the formula will be used.
𝐶𝐸 = 𝐷𝑃 + 𝐴 or 𝐶𝐸 = 𝐷𝑃 + 𝑅
1−(1+𝑖)−𝑛
𝑖

9. Example 1
Determine the amount and present value
of an ordinary annuity of P 500 each quarter
payable for 6 years and 9 months, if money is
worth 14% compounded quarterly.

10. Example 2
A computer set is offered for sale for P
15,000 down payment and P 2,500 every 3
months for the balance for 2 years and 6 months,
if interest is to be computed at 11% compounded
quarterly, what is the cash equivalent of the
computer set?

11. Example 3
What must be deposited every 6 months in a
fund paying 15% compounded semi-annually in
order to have P 50,000 in 9 years?

12. Example 4
What sum will be paid at the end of every
month for 8 years and 6 months if the present
value of P 20,200 and interest are paid at 12 %
compounded monthly?