Annuities I - Ordinary Annuity

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Basic present value analysis is used to determine the present value of a single sum to be received (paid) some time in the future - for example, a note receivable.  However, sometimes you expect to receive (or pay) a series of payments - interest on a bond or payments on a car loan, for example   In that case we must deal with the following:
  • regular payments
  • made or received at regular intervals
  • at least once a year, but may be semi-annually (bond interest) or monthly (car payment)

For example:

  • What is the present value of three payments of $100 each.  The payments will be received at the end of each of the next three years.  We want to earn 10% interest on our investment.
Option 1 we could express and solve the question above as follows:
 

receive

PV

Factor

answer:

$100.00

(10%,1)

0.9091

$90.91

$100.00

(10%,2)

0.8264

$82.64

$100.00

(10%,3)

0.7513

$75.13

$248.68
While this is certainly doable, it becomes very tiresome (imagine a 50 year bond with semi-annual interest payments - you would have to the calculation 100 times!  Instead, we can use Algebra (uuhh, there it is again!) - we factor out the constant ($100)
 

Option 2: Restated question:

Present value of an annuity: (PVa)

  

$100 * (.9091 + . 8264 + .7513) = X

$ 100 * 2.4868 = X = $248.68

(.9091 + . 8264 + .7513) = 2.4868 = Pva(10%, 3)
While this is much nicer, it is still too boring.   Instead just use the present value table for an ordinary annuity (D38 in Nikolai) 2.486852 for PVa (10%, 3).  Or, use the appropriate function in a spreadsheet program or calculator (But not on the exam!):
Option 3: $100 * PVa(3,10%) = $100*2.486852 = $248.69

Annuity Due
What is an annuity due? continue to annuities II

return to: home| basic PV  | pv & accounting | annuities I  |  annuities II | Examples: 1 - PV of Note Receivable | 2 - Issuance of Bond | 3: Cash or Note Payable? | 4 A: Buying a car - interest rate? |4 B: Buying a car - payments: | Quizz Practice quizz (from an old text book, but still working)