## 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).