Simple Interest F
( 1+i )n−1 =R
I-Interest
P- Principal / Present Value/ Loan/ Amount borrowed /
F=R ( i ) ( ( 1+i )n−1
i )
use to solve for cash value
t- term in years
P
r- interest rate (%) 1−( 1+i )−n =R
F-future value/ savings P=R ( i )( 1−( 1+i )−n
i )
I =Prt
I I I Cash Value = Down Payment + Present Value
=P , =r , =t
rt Pt Pr CV= DP + PV
Use the formula for P to solve for cash value or cash
I =F−P price
F=P+ I
Deferred Annuity
Some Key words: simple interest rate Some Key words: “First payment is due”, “it is
F=P ( 1+ rt ) deferred for”
F F 1−( 1+i )−n
F
1+ rt
=P , P
−1
t
=r
, P
−1
r
=t
P¿ =R ( i ) ( 1+i )−d
P¿
−n
=R
1−( 1+i )
Compound interest
Some Key Words: compounded ( i )( 1+i )−d
monthly/semiannually/every 4 months
i-interest rate General Annuities
j- nominal rate Some Key Words:
m- frequency of conversion The money is compounded monthly, then the payment
n-total number of conversion is done quarterly.
number of interest compoundings per year
c=
n j number of payments per year
F=P ( 1+ i ) , i= , n=tm
m i 2=¿
F The formula differs depending if it is compound
=P
( 1+ i )n interest, compounded continuously, ordinary annuity,
F n
1 or deferred annuity. There will only be changes in the
i= ( )
P
−1 , j=i m value of i.
F
n=
log ( )P
,t =
n
Amortization
Outstanding Balance
log ( 1+i ) m Prospective (n is known)
1−( 1+i )−(n−k )
Compounded Continuously
F=P e
jt
O B k ⇒ Pn −k =R [ i ]
Retrospective (n is unknown)
( 1+i )k −1
Ordinary Annuity
Some Key words: Compounded monthly paid every/
k
O B k =P ( 1+i ) −R [ i ]
each month. Total Interest: TI =nR−L
R- periodic payment/ installment Interest for the kth payment : I k =O B k−1 i
Repayment for the kth period: R Pk =R−I k
( 1+i )n−1 =R
I-Interest
P- Principal / Present Value/ Loan/ Amount borrowed /
F=R ( i ) ( ( 1+i )n−1
i )
use to solve for cash value
t- term in years
P
r- interest rate (%) 1−( 1+i )−n =R
F-future value/ savings P=R ( i )( 1−( 1+i )−n
i )
I =Prt
I I I Cash Value = Down Payment + Present Value
=P , =r , =t
rt Pt Pr CV= DP + PV
Use the formula for P to solve for cash value or cash
I =F−P price
F=P+ I
Deferred Annuity
Some Key words: simple interest rate Some Key words: “First payment is due”, “it is
F=P ( 1+ rt ) deferred for”
F F 1−( 1+i )−n
F
1+ rt
=P , P
−1
t
=r
, P
−1
r
=t
P¿ =R ( i ) ( 1+i )−d
P¿
−n
=R
1−( 1+i )
Compound interest
Some Key Words: compounded ( i )( 1+i )−d
monthly/semiannually/every 4 months
i-interest rate General Annuities
j- nominal rate Some Key Words:
m- frequency of conversion The money is compounded monthly, then the payment
n-total number of conversion is done quarterly.
number of interest compoundings per year
c=
n j number of payments per year
F=P ( 1+ i ) , i= , n=tm
m i 2=¿
F The formula differs depending if it is compound
=P
( 1+ i )n interest, compounded continuously, ordinary annuity,
F n
1 or deferred annuity. There will only be changes in the
i= ( )
P
−1 , j=i m value of i.
F
n=
log ( )P
,t =
n
Amortization
Outstanding Balance
log ( 1+i ) m Prospective (n is known)
1−( 1+i )−(n−k )
Compounded Continuously
F=P e
jt
O B k ⇒ Pn −k =R [ i ]
Retrospective (n is unknown)
( 1+i )k −1
Ordinary Annuity
Some Key words: Compounded monthly paid every/
k
O B k =P ( 1+i ) −R [ i ]
each month. Total Interest: TI =nR−L
R- periodic payment/ installment Interest for the kth payment : I k =O B k−1 i
Repayment for the kth period: R Pk =R−I k
