Annuities Formula
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If A is given If S is given A =R [ 1−( 1+i ) −n i ] S=R [ ( 1+i ) n −1 i ] p.104 Find R: R= [ A i 1−( 1+i) −n ] p.104 Find R: R= [ S i ( 1+i) n −1 ] p.104 Find t: n= −log [ 1− Ai R ] log ( 1+i ) p.106 n = tm tm = −log [ 1− Ai R ] log( 1+i) tmx 1 m = 1 m − log [ 1− Ai R ] log( 1 +i) t= −log [ 1− Ai R ] m log( 1+i) Find t: n= log [ 1+ Si R ] log( 1 +i) p.106 n = tm tm = −log [ 1− Si R ] log( 1 +i) tm x 1 m = 1 m − log [ 1− Si R ] log ( 1 +i) t= log [ 1+ Si R ] m log ( 1+ i) If A is given If S is given Find j: (pp.109-110) ( n ¿¿ 2− 1)i 2 +6 ( n +1) i +12 ( 1− nR A ) =0 ¿ ai 2 + bi+ c=0 In quadratic equation form: i= −b± √ b 2 −4 ac 2 a Find j: (pp.109-110) ( n ¿¿ 2− 1) i 2 −6 ( n−1) i +12 ( 1− nR S ) =0 ¿ ai 2 −bi +c=0 In quadratic equation form: i= −b± √ b 2 −4 ac 2 a
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Annuities Formula (BUSANA1)
Transcript of Annuities Formula
If A is given If S is given
A=R[ 1−(1+ i )−n
i ] S=R [ (1+i )n−1i ] p.104
Find R:
R=[ Ai1−(1+i)−n ] p.104
Find R:
R=[ Si(1+i)n−1 ] p.104
Find t:
n=−log [1− AiR ]log (1+i)
p.106
n = tm
tm=−log [1− AiR ]log(1+i)
tm x1m
= 1m
−log [1− Ai
R ]log(1+i)
t=−log [1− AiR ]m log(1+i)
Find t:
n=log [1+ SiR ]log(1+i)
p.106
n = tm
tm=−log [1−SiR ]log(1+ i)
tm x1m
= 1m
−log [1− SiR ]log(1+i)
t=log [1+ SiR ]m log(1+i)
If A is given If S is givenFind j: (pp.109-110)
(n¿¿2−1) i2+6(n+1) i+12(1−nRA )=0¿a i2+bi+c=0
In quadratic equation form:
i=−b±√b2−4ac2a
i= jmj=im
Find j: (pp.109-110)
(n¿¿2−1) i2−6(n−1)i+12(1−nRS )=0¿a i2−bi+c=0
In quadratic equation form:
i=−b±√b2−4ac2a
i= jmj=im
Ordinary Annuity – periodic payment is made at the start of each term or period
Annuity Due - periodic payment is made at the beginning of each term or period
Deferred Annuity-periodic payment does not occur at the start or end of the term or period but delayed to a later date
Present Value
A=R[ 1−(1+ i )−n
i ] A=R+R[ 1−(1+i )−(n−1)
i ]or
A=A (1+i) p. 112-113
or
A=R[ 1−(1+ i )−n
i ](1+ i)
A=R[ 1−(1+ i )−n
i ](1+ i)−d
orA=A (1+i)−d
Future Value or Amount
S=R [ (1+i )n−1i ] p.104 S=R [ (1+i )(n+1)−1
i ]−Ror
S=S (1+i)or
S=R [ (1+i )n−1i ](1+i)
S=R [ (1+i )n−1i ]
Ordinary Annuity Annuity Due Deferred Annuity
If A is given
A=R[ 1−(1+ i )−n
i ]Find R
R=[ Ai1−(1+i)−n ]
Find t
t=−log [1− AiR ]m log(1+i)
If A is given
A=R[ 1−(1+ i )−n
i ](1+ i)Find R
R=¿Find t
t=−log [1− A i
R (1+i ) ]m log(1+i)
A=R[ 1−(1+ i )−n
i ](1+ i)−d
Find RIf A is given
R=[ A
(1−(1+ i)−n )(1+ i)−d ]
If S is given
S=R [ (1+i )n−1i ] p.104
Find R
R=[ Si(1+i)n−1 ]
Find t
t=log [1+ SiR ]m log(1+i)
If S is given
S=R [ (1+i )n−1i ](1+i)
Find R
R=[ S i(1+i ¿¿¿n−1 )(1+i) ]
Find t
t=log [1+ S i
R (1+i ) ]m log(1+i)
S=R [ (1+i )n−1i ]
Find R (if S is given)
R=[ S i(1+i ¿¿¿n−1 ) ]
ANNUITY’S VALUE AT ANY TIME
Before the start of the term ( A ¿¿ After the end of the term (Y ¿ At the middle of the term (X ¿
To find A:1. Find the present value
(A) of an ordinary annuity
2. Then discount A by using the formula
A=A (1+i)−d
To find Y:1. Find the amount (S) of
an ordinary annuity
2. Then accumulate S by using the formula:
Y=S¿
To find X:1. Find the amount (S) at
the end of the kth period and the remaining liability after the kth period
2. Then use the formula:
X=S K+RLK
