ABSTRACT
Let i = interest rate per period n = number of interest (payment) periods P = present sum of money (present worth) F = sum of money at the end of n periods from the present date that is
equivalent to P at interest rate i (F = future worth) A = uniform end-of-period payment continuing for n periods that in
total is equivalent to P at interest rate i (A = annuity)
Then
( )1 nF P i= + (20.1)
1 1
i i A P
i
⎛ ⎞+ = ⎜ ⎟⎜ ⎟+ −⎝ ⎠
(20.2)
Let Ek = portion of A in period k paid against principal (Ek = equity payment) Ik = portion of A in period k paid as interest (Ik = interest payment)
Then
1 1
k n kE A i − + ⎛ ⎞
= ⎜ ⎟⎜ ⎟+⎝ ⎠ (20.3)
1 1
⎛ ⎞ = −⎜ ⎟⎜ ⎟+⎝ ⎠
(20.4)
Grant, Ireson, and Leavenworth (1982, p. 33); White, Agee, and Case (1977, pp. 65, 92, 93).
