Formulas Discount Factors  
Factor Name (click for graphic)  Converts  Symbol  Formula 
Single Payment Compound Amount  to F given P  (F/P, i%, n)  (1 + i)^{n} 
Single Payment Present Worth  to P given F  (P/F, i%, n)  (1 + i)^{n} 
Uniform Series Sinking Fund  to A given F  (A/F, i%, n)  i / [(1 + i)^{n} 1] 
Capital Recovery  to A given P  (A/P, i%, n)  i (1 + i)^{n} / [(1 + i)^{n} 1] 
Uniform Series Compound Amount  to F given P  (F/A, i%, n)  [(1 + i)^{n} 1]/ i 
Uniform Series Present Worth  to P given A  (P/A, i%, n)  [(1 + i)^{n} 1]/ [i(1 + i)^{n}] 
Uniform Gradient Present Worth  to P given G  (P/G, i%, n)  [(1 + i)^{n} 1]/ [i^{2}(1 + i)^{n}]  n/[i(1+i)^{n}] 
Uniform Gradient Future Worth  to F given G  (F/G, i%, n)  [(1 + i)^{n} 1]/ i^{2}  n/i 
Uniform Gradient Uniform Series  to A given G  (A/G, i%, n)  1/i  n/[(1 + i)^{n} 1] 
A .....Uniform amount per interest period F .......Future worth, value, or amount G ......Uniform gradient amount per interest period P ......Present worth, value or amount n ..... at time n i ...... interest rate per interest period 

Single Payment Compound Amount
(future value, compound interest) 



Single Payment Present Worth (present value) The present value (P) of a future amount (F) based on (n) compounding periods at interest rate (i) per period. For continuous compounding; r = nominal annual interest rate, and n = years 



Uniform Series Sinking Fund (payments) The uniform series payment/investment (A) required to be made every period for (n) periods, at interest rate (i) per period to produce a future amount (F). For continuous compounding; r = nominal annual interest rate, and n = years 

Uniform Series Compound Amount (Annuity) The future amount (F) for making a uniform series payment/investment (A) every period for (n) periods, at interest rate (i) per period. For continuous compounding; r = nominal annual interest rate, and n = years 

Capital Recovery (Amortization) The series of uniform payment, income, or amount (A) required for n periods at interest rate (i) per period to pay off a debt or to recover an initial capital investment (P). For continuous compounding; r = nominal annual interest rate, and n = years 

Uniform Series Present Worth (Annuity) The present value (P) of a series of uniform payments (A) to be made for (n) periods at interest rate (i) per period. For continuous compounding; r = nominal annual interest rate, and n = years 

Uniform Gradient Present Worth The present value (P) of a series of uniform gradient payments (G) to be made for (n) periods at interest rate (i) per period. 

Uniform Gradient Future Worth The future value (F) of a series of gradient payments (G) to be made for (n) periods at interest rate (i) per period. 

Uniform Gradient Uniform Series The uniform payment (A) of a series of gradient payments (G) to be made for (n) periods at interest rate (i) per period. 

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