# Compound Interest Formulas - PDF

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Interest Factor Formulas

Compound Amount:

To find F, given P      (F/P, i, n)       F = P(1 + i ) n

Present Worth:

To find P, given F      (P/F, i, n)       P = F (1 + i ) − n

Series Compound Amount:
 (1 + i ) n − 1
To find F, given A      (F/A, i, n)       F = A               
       i       

Sinking Fund:
       i     
To find A, given F      (A/F, i, n)        A = F             
 (1 + i ) − 1
n

Capital Recovery:
 i (1 + i ) n 
To find A, given P      (A/P, i, n)        A = P              
 (1 + i ) − 1
n

Series Present Worth:
 (1 + i ) n − 1
To find P, given A      (P/A, i, n)       P = A            n 
 i (1 + i ) 

 (1 + i ) n − in − 1
To find A, given G      (A/G, i, n)      A = G                     
 i (1 + i ) − i 
n

1           n      
or A = G  −                 
 i (1 + i ) − 1
n

 (1 + i ) n − in − 1
To find P, given G      (P/G, i, n)       P = G 2                  
 i (1 + i )
n


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To find P, given A1, g           (P/G, g, i, n)                 [
P = A1 n(1 + i ) −1   ]
when i = g

1 − (1 + g ) n (1 + i ) − n 
P = A1                             
         i−g                
when i / g

Continuous Compounding at Nominal Rate r

Single Payment:                        [ ]
F = P e rn                              [ ]
P = F e − rn

 er − 1                       e rn (e r − 1) 
Uniform Series:                 A = F  rn                    A = P  rn             
 e − 1                        e −1 

 e rn − 1                     e rn − 1 
F = A r                      P = A rn r      
 e −1                         e (e − 1) 

Compound Interest
i = Interest rate per interest period*.
n = Number of interest periods.
P = A present sum of money.
F = A future sum of money.
A = An end-of-period cash receipt or disbursement in a uniform series continuing for n
periods.
G = Uniform period-by-period increase or decrease in cash receipts or disbursements.
g = Uniform rate of cash flow increase or decrease from period to period; the geometric
r = Nominal interest rate per interest period*.
m = Number of compounding subperiods per periods*.
_________________
*Normally the interest period is one year, but it could be something else.

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Effective Interest Rates
m
         r
For non-continuous compounding:       ieff or ia = 1 +      −1
         m

where   r = nominal interest rate per year
m = number of compounding periods in a year

OR

ieff or ia = (1 + i ) − 1
m

where i = effective interest rate per period
m = number of compounding periods in a year

For continuous compounding:                      ( )− 1
ieff or ia = e
r

where   r = nominal interest rate per year

Values of Interest Factors When n Equals Infinity

Single Payment:                   Uniform Payment Series:

(F/P, i, ∞) = ∞                    (A/F, i, ∞) = 0
(P/F, i, ∞) = 0                    (A/P, i, ∞) = i
(F/A, i, ∞) = ∞
(P/A, i, ∞) = 1/i

(A/G, i, ∞) = 1/i
(P/G, i, ∞) = 1/i2

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