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7/26/2019 Lesson 4 - Annuity (Ordinary).pptx
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Annuities
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Annuity is a series/sequence ofpayments (usually equal) made at equal
intervals of time.
Installment payments
Monthly payments/rentals
Insurance premiums
Monthly retirement benefits Weekly / monthly waes
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Types of Annuity
1.Annuity Certain Annuity payable for a denite duration
Payments begin and end at xed times
2. Contingent Annuity orAnnuity Uncertain
Annuity payable for an indenite
duration (beginning or termination isdependent on some certain event)
Payments are not certain to be made
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Kinds of Annuity Certain
Simple AnnuityThe interest conversion
period () is eual to the
payment interval ()
General AnnuityThe interest conversion
period () is not eual tothe payment interval ()
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Classication of SimpleAnnuity
Ordinary Annuity
Annuity in "hich periodic payment () is made atthe endof each payment interval.
Annuity Due()Annuity in "hich periodic payment () is made atthe beginningof each payment interval
Deferred Annuity()Annuity in "hich periodic payment () is neither atthe beginning nor end of each payment intervalbut some later date.
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!OR"U#AS
!inding ! $%en gi&en A !inding A $%engi&en !
Finding P when given A Finding A whengiven P
#ource$ #ullivan% &illiam '.% lin . &ic*s and +ames T. ,uxho-. (2/). 0'00' 34045%16T78. Pearson9Prentice 7all. p1:916
+=
i
iAF
n 1)1(
+
+=
n
n
ii
iAP
)1(
1)1(
+=
1)1( ni
iFA
+
+=
1)1(
)1(n
n
i
iiPA
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!OR"U#AS
Finding F when given A Finding A whengiven F
Finding P when given A Finding A whengiven P
#ource$ #ullivan% &illiam '.% lin . &ic*s and +ames T. ,uxho-. (2/). 0'00' 34045%16T78. Pearson9Prentice 7all. p1:916
+=
i
iAF
n 1)1(
+
+=
n
n
ii
iAP
)1(
1)1(
+=
1)1( ni
iFA
+
+=
1)1(
)1(n
n
i
iiPA
;niform
#eries3ompound
amountfactor
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!OR"U#AS
Finding F when given A Finding A whengiven F
Finding P when given A Finding A whengiven P
#ource$ #ullivan% &illiam '.% lin . &ic*s and +ames T. ,uxho-. (2/). 0'00' 34045%16T78. Pearson9Prentice 7all. p1:916
+=
i
iAF
n 1)1(
+
+=
n
n
ii
iAP
)1(
1)1(
+=
1)1( ni
iFA
+
+=
1)1(
)1(n
n
i
iiPA
#in*ingfund factor
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!OR"U#AS
Finding F when given A Finding A whengiven F
Finding P when given A Finding A whengiven P
#ource$ #ullivan% &illiam '.% lin . &ic*s and +ames T. ,uxho-. (2/). 0'00' 34045%16T78. Pearson9Prentice 7all. p1:916
+=
i
iAF
n 1)1(
+
+=
n
n
ii
iAP
)1(
1)1(
+=
1)1( ni
iFA
+
+=
1)1(
)1(n
n
i
iiPA
;niformseries
present
"orth factor
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!OR"U#AS
Finding F when given A Finding A whengiven F
Finding P when given A Finding A whengiven P
#ource$ #ullivan% &illiam '.% lin . &ic*s and +ames T. ,uxho-. (2/). 0'00' 34045%16T78. Pearson9Prentice 7all. p1:916
+=
i
iAF
n 1)1(
+
+=
n
n
ii
iAP
)1(
1)1(
+=
1)1( ni
iFA
+
+=
1)1(
)1(n
n
i
iiPA3apital
recoveryfactor
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A man deposits P 12%2every end of / months in anaccount paying
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A car "as bought "ith ado"n payment of P2%and P1@% at the end ofevery month for 6 years to
discharge all principal andinterest at the rate of 12=compounded monthly. ind
the cash value of the car.
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An ,8 television set ispurchased "ith a do"npayment of P6% and
P:%/2:.
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rs. AlvareB pays P2
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!ow much monthly deposit must be
made for " years and " months in
order to accumulate # $%&'&&& at
$" compounded monthly
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What sum will be paid at the end of
each quarter for * years and * months'
if the present value is # "&'"&& andinterest is paid at $& compounded
quarterly
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+ino wants to buy a car worth
#,-&'&&&. !e can pay -& of the
price as down payment and the balance
payable every end of the month for *&
months' how much must he pay
monthly at $" compounded monthly
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#am wants to have # ,"&'&&& at the endof " years for her raduation epenses.
he plans to deposit a certain sum' to
achieve this at the end of each month.If her bank pays $" compounded
monthly' what should be the amount of
her monthly deposit
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!ow much must be paid for -0 monthsto settle an obliation of # $%1'-&&' if
money is worth $% compounded
monthly
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7/26/2019 Lesson 4 - Annuity (Ordinary).pptx
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$. A man deposits #$%'%&&every end of * months in
an account payin " 2
compounded semi3annually. What amount is
in the account at the end of
4 years and * months
SEATWORK
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%. A home video entertainment set
is offered for sale for #$0'&&&
down payment and #$0&& every 1
months for the balance' for $0
months. If interest is to be
computed at $& converted
quarterly' what is the cash priceequivalent of the set
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3. On May 31, 2007, Connie invested P
185,000 at 10 !o"#o$nded "ont%&y.
T%e invest"ent is to 'e #aid o$t in (0
e)$a& "ont%&y #ay"ents *it% t%e +ist
#ay"ent on -$ne 30,2007. W%at is t%e
sie o+ ea!% "ont%&y #ay"ent/
. Co!oy *ants to a!!$"$&ate P 230,000 in
(.5 yeas. E)$a& de#osits ae "ade at t%eend o+ ea!% )$ate in an a!!o$nt t%at
#ays 15 !o"#o$nded )$ate&y. W%at
is t%e sie o+ ea!% de#osit/
7/26/2019 Lesson 4 - Annuity (Ordinary).pptx
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indin t%e
4TEREST RATEo+ an Ann$ity
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$.) olve for i usin the quadratic formula5
67ype $5 use the minus sin of the quadratic formula
67ype %5 use the plus sin of the quadratic formula
%. After solvin for ' find 5
where Type I: F and A aregiven
Type II: P and Aare given
a
b
c
where Type I: F and A aregiven
Type II: P and Aare given
a
b
c
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8.A. 9orporation is plannin to
create a fund by depositin
#$'"%& every quarter for 0 years
in a bank that promises to pay afied rate over the entire term.
:ind the rate converted quarterly
if the amount in the fund at theend of the term is #*&'&&&.
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;ovo
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At $%at nominal ratecompounded (uarterly ist%e loan of )*+,--- .e paid
$it% e(ual payment of)/,*-- at t%e end of eac% 0mont%s for 1 years2
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If # "'&"& periodic payment per
quarter for $& 2 years amount to #
""&'&&&= what is the rate of
interest
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$.) If # "'&"& periodic payment per quarter for $& 2
years amount to # ""&'&&&= what is the rate ofinterest
%.) :ind the interest rate compounded semi3annually
on #--'-&& whose periodic deposit of # -'-&&every end of si months for * years and * months.
1.) A dinin set worth # $%'%&& cash is purchased by
a down payment of # "'0&& and monthly paymentof #"0& for $0 months. :ind the rate of interest
compounded monthly.
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-.) An item can be purchased for # $-'"&& or
for # 1'0&& down payment and installment
payment of # $'&1& for 1* months. :ind theinterest rate compounded semi3 annually.
".) A trust fund is to be formed by depositin#-'"&& every quarter for " 2 years in a bank
that promises to pay a fied rate over the
entire term. If the amount of the fund at the
end of the term is # 0"'&&& find the rate
compounded quarterly.
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:indin the 7>?M of
an Annuity
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+oro borrows #%&'&&& with interestat "." compounded quarterly. !e
arees to pay #0"& at the end of
each quarter. !ow lon must hepay
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Ms. Marie Abellar invest her retirementbenefits of 1.0 million at 4
compounded monthly. If she withdraws
the money in monthly payments of
#"&'&&&' how many reular payments
will she et
7/26/2019 Lesson 4 - Annuity (Ordinary).pptx
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:ind the time and the number of semi3
annual payments of #-0& each and the
concludin deposit' which must be made
to accumulate #$0'"&&' if money earns
interest at , compounded semi3
annually.
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A man deposits # "'%&& at the end
of each three months in an account
payin $- converted quarterly. In
order to accumulate #$&"'&&&' howmany reular deposit every quarter
must he make and what is the si@e of
the concludin payment' if one isneeded
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Annuity Due ' !ormulas
Finding F when given A
Finding P when given A
+=
+
11)1( 1
i
iAF
n
++= + 1)1(1
1
i
iAP
n