# .Xls Formula for Compound Interest by jlu62532

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```									Compound Interest Tables
(Spreadsheet format developed by V. Dean Adams, University of Nevada Reno)
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 , ∞) = ∞
Arithmetic Gradient Series:                                                (P/A , i , ∞) = 1/i
(A/G , i , ∞) = 1/i
(P/G , i , ∞) = 1/i 2                                                                          Nomenclature and Definitions           Non-Annual Compounding
m
A…    Uniform amount per interest                ⎛    r ⎞
i e = ⎜1 +   ⎟        −1
Factor Name              Converts               Symbol                     Formula                     period                                     ⎝    m ⎠
Single Payment            to F given P           (F/P, i%, n)                 (1 + i)n              B…    Benefit                                Discount Factors for
Compound                                                                                                                                      Continuous Compounding
Single Payment            to P given F           (P/F, i%, n)                 (1 + i)-n             BV …    Book value                        (n is the number of years)
Present Worth
Uniform Series            to A given F          (A/F, i%, n)                   i                    C…      Cost                                 (F/P, r%, n) = er n
Sinking Fund                                                            [(1 + i)    n
− 1]
Uniform Series            to A given P          (A/P, i%, n)              i(1 + i) n                d…      Combined interest rate per           (P/F, r%, n) = e-r n
Capitol Recovery                                                       [(1 + i) n − 1 ]                     interest period
Uniform Series            to F given A          (F/A, i%, n)               [(1 + i) n − 1]          Dj …    Depreciation in year j                              er −1
(A/F, r%, n) =
Compound                                                                           i                                                                            er n −1
Uniform Series            to P given A          (P/A, i%, n)             [(1 + i) n − 1 ]           F…      Future worth, value or                              er n −1
(F/A, r%, n) =
Present Worth                                                               i(1 + i) n                      amount                                              er −1
Uniform                   to P given G          (P/G, i%, n)       [(1 + i) n − 1]
−
n        f…      General inflation rate per                      er −1
i(1 + i) n
(A/P, r%, n) =
Gradient**                                                           i 2 (1 + i) n                          interest period                                1 - e -r n
Uniform Gradient†         to F given G          (F/G, i%, n)          [(1 + i) n − 1]   n           G…      Uniform gradient amount                        1 - e -r n
−                                                      (P/A, r%, n) = r
2                             per interest period
Future Worth                                                                i           i                                                                   e −1
Uniform                   to A given G          (A/G, i%, n)           1          n                 i…      Interest rate per interest
−
i   [(1 + i) n − 1]
ie …    Annual effective interest rate
Subscripts
j…       at time j                                                                                  m…      Number of compounding
periods per year                      BOOK VALUE
n…         at time n                                                                                n…      Number of compounding               BV = initial cost – ΣDj
periods; of the expected life
** …       P/G = (F/G)/(F/P) = (P/A)x(A/G)                                                          P…      Present worth, value or
amount
†          F/G = (F/A – n)/i = (F/A)x(A/G)                                                          r…      Nominal annual interest rate
…

††         A/G = [1 – n(A/F)]/i                                                                     Sn …    Expected salvage value in
…
year n

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