UNIT 2

ANNUITY
 ANNUITY
Annuity – a series of equal
payments made at equal
intervals of time.
Examples:
daily wages, monthly rents,
annual insurance premiums
 ELEMENTS OF ANNUITY
Elements of Annuity:
1. Sequence or Series of Payments
2. Payments are of equal amounts
3. Payments are made at an equal
interval of time.
 ELEMENTS OF ANNUITY
If one of the elements is
missing, the payment is not
considered as an annuity.
A series of payments of equal
amounts but made at
unequal interval of time is
not an annuity.
 ELEMENTS OF ANNUITY
A series of payments of
unequal amounts made at
equal intervals of time is not
an annuity.
 DEFINITION OF KEY
TERMS
Term – refers to the period of time
from the beginning of the first
payment interval up to the last
payment interval.
Periodic Payment – the size or
value of each payment
Payment Interval – the time
between two successive
payments
 KINDS OF ANNUITY
1. Annuity Certain
2. Annuity Uncertain
3. Ordinary Annuity
4. Annuity Due
5. Deferred Annuity
6. Simple Annuity
7. Complex Annuity
 KINDS OF ANNUITY
Annuity Certain – an annuity with
definite term. The first and last
payment intervals have definite
dates.
Example – payments of household
appliances
 KINDS OF ANNUITY
Annuity Uncertain / Contingent
Annuity– an annuity with an
indefinite term. The first payment
interval has a definite date, but the
last payment interval cannot be
determined.
Example – health insurances
Contingent Annuities - Annuities certain - have a
have no fixed number of specific stated number of
payments but depend on payments
an uncertain event

Life Insurance payments Mortgage payments

 KINDS OF ANNUITY
Ordinary Annuity – an annuity where
periodic payments are made at the
end of the payment interval.
Example – buying a house at an
instalment price
 KINDS OF ANNUITY
Annuity Due– an annuity where
periodic payments are made at the
beginning of the payment interval.
 Annuity due -
Ordinary annuity - regular
regular deposits/payments
deposits/payments made at the
made at the end of beginning of the
the period period

Jan. 31 Monthly Jan. 1

June 30 Quarterly April 1
Dec. 31 Semiannually July 1
Dec. 31 Annually Jan. 1
 KINDS OF ANNUITY
Deferred Annuity– an annuity where
the first periodic payment begins
other than the first payment
interval.
 KINDS OF ANNUITY
Simple Annuity– an annuity where
payment intervals coincide with the
interest compounding period.
 KINDS OF ANNUITY
Complex Annuity– an annuity where
payment intervals do not coincide
with the interest compounding
period.
 ORDINARY ANNUITY
If the time of periodic payments is not
stated, it is understood that
payments are made at the end of
each payment interval. Therefore, it
is considered as an ordinary annuity.
 ORDINARY ANNUITY
Ordinary Annuity – an annuity where
periodic payments are made at the
end of the payment interval.
Example – buying a house at an
instalment price
 ORDINARY ANNUITY
Amount of ordinary annuity – equal to
the sum of the compound amounts
of several payments from the first
interval payment to the end of the
term.
The, amount of an ordinary annuity
therefore, refers to the future value
of compounded periodic payments
and the compound interest for a
given period of time.
ORDINARY ANNUITY
FORMULA DERIVED
 FORMULA DERIVED
F = A {[(1+i)n – 1] / i}
P = {A[(1+i)n – 1]/[i(1+1)n]}
where:
F = Future Value
A = amount of each payment of ordinary
annuity
n = number of payments
i = interest per compounding period
 SAMPLE PROBLEM
Find the amount of a Php5,000
ordinary annuity payable every
month at 9% compounded monthly
for 3 years.
 SAMPLE PROBLEM
A portable digital music player is
purchased with a down payment off
Php1000 and the balance at
Php1,075.83 a month for 1 year.
What is its cash price if its interest
rate is 6% converted monthly?
 SAMPLE PROBLEM
An ordinary annuity payable quarterly
at 13% compounded every 3 months
for 4 years and 9 months has a
present value of Php75,000. How
much is the quarterly payment?
 SAMPLE PROBLEM
Merly borrowed P60,000 payable on
instalment of Php15,000 at the end
of every quarter. If money is worth
12% compounded quarterly, how
long will it take her to pay the debt
and interest?
 SAMPLE PROBLM
Irene is setting up a fund of Php60,000
to purchase a computer. If she
deposits Php12,000 in a bank every
end of the quarter, which pays an
interest of 12% compounded
quarterly, how long will it take her to
raise the desired amount?
 Term of the annuity - the
Annuity - A series of time from the beginning of
payments the first payment period to
the end of the last
payment period.

Present value of an
Future value of annuity - annuity - the amount of
the future amount of a
money needed to invest
series of payments plus
interest today in order to receive
a stream of payments
for a given number of
years in the future
 ANNUITY DUE
Annuity Due– an annuity where
periodic payments are made at the
beginning of the payment interval.

If the first payment is made at the

beginning of the first payment
period, the end of the term is one
payment interval after the last
periodic payment.
 ANNUITY DUE
Amount of annuity due – accumulated
value of all periodic payments from
the first payment interval up to the
end of the term.
ANNUITY DUE FORMULA
DERIVED
 FORMULA DERIVED
F = A {[(1+i)n – 1] / i}(1+i)
P = {A[(1 - (1+i)-n)/i](1+i)}
where:
F = Future Value
A = amount of each payment of ordinary
annuity
n = number of payments
i = interest per compounding period
 SAMPLE PROBLEM
Mae deposited Php10,000 every
beginning of the quarter for 1 year at
12% compounded quarterly.
Compute the amount of the annuity
due and the present value of the
annuity.
 SAMPLE PROBLEM
A television set is being sold for
Php20,000 and can be bought on
quarterly instalment payments for
one year with the condition that
payments should be made at the
beginning of each quarter. What is
the quarterly instalment payment if
the interest rate is 10% compounded
quarterly?
 SAMPLE PROBLEM
The present value of the annuity due is
Php20,000 with a quarterly periodic
payment at the beginning of each
quarter of Php2,300.00 at 10%
compounded quarterly. Find the term
of the annuity due.
 DEFERRED ANNUITY
Deferred Annuity– an annuity where
the first periodic payment begins
other than the first payment
interval.
 DEFERRED ANNUITY
The amount of deferred annuity – the
sum of all periodic payments,
including the interest from the first
interval payment to the end of the
term.
ANNUITY DUE FORMULA
DERIVED
 FORMULA DERIVED
F = A {[(1+i)n – 1] / i}
P = {A[(1+i)n – 1]/[i(1+i)n]}
P = {A[1- (1+i)n ]/i}(1+i)-k
where:
F = Future Value
A = amount of each payment of ordinary
annuity
n = number of payments
i = interest per compounding period
k = period of deferment
 SAMPLE PROBLEM
Find the present value of an annuity of
Php8000 made at the end of every
quarter for 1 year if money is worth
10% compounded quarterly. The
periodic payment is deferred for two
quarters.
 SAMPLE PROBLEM
Yvonne borrows Php28,645 at 10%
compounded quarterly. She will
make a series of quarterly periodic
payments for 1 year, and the first
quarterly payment is made at the
end of third quarter from now.