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Annuities and loans

Annuities and perpetuities

Value level payment streams with formulas and with PV() and FV().

17 minintermediateMembers

Learning objectives

  • Value an ordinary annuity and an annuity due
  • Use PV() and FV() and their sign convention
  • Value a perpetuity
  • Value an annuity that starts in a later year

An annuity is a series of equal payments at regular intervals: lease payments, loan installments, pension income. Payments at the end of each period form an ordinary annuity; payments at the start form an annuity due.

Present value of an ordinary annuity

PV = PMT × [1 − (1 + r)⁻ⁿ] ÷ r

PMT
payment per period
r
rate per period
n
number of payments

Included with a Formula Quest membership

The rest of this lesson is for members. Members get the full lesson, including its 4 graded exercises, and every other Finance Quest lesson.