Home > Economics & Finance > Future Value of Annuities And Annuity Due

Future Value of Annuities And Annuity Due

Future Value of Annuities

An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples.  The payments or receipts occur at the end of each period for an ordinary annuity    while they occur at the beginning of each period.for an annuity due.

Future Value of an Ordinary Annuity (FVoa)

The Future Value of an Ordinary Annuity (FVoa) is the value that a stream of expected or promised future payments will grow to after a given number of periods at a specific compounded interest.

The Future Value of an Ordinary Annuity could be solved by calculating the future value of each individual payment in the series using the future value formula and then summing the results. A more direct formula is:

FVoa = PMT [(((1 + i)^n) – 1) / i]

Where:
    FVoa = Future Value of an Ordinary Annuity
    PMT = Amount of each payment
    i = Interest Rate Per Period
    n = Number of Periods

Example: What amount will accumulate  if we deposit $5,000 at the end of each year for the next 5 years?  Assume an interest of 6% compounded annually.

PV = 5,000 i = .06 n = 5

FVoa = 5,000 [ (1.3382255776 – 1) /.06 ] = 5,000 (5.637092) = 28,185.46

Year                 1              2              3              4              5
Begin                0    5,000.00  10,300.00  15,918.00  21,873.08
Interest             0      300.00      618.00       955.08    1,312.38
Deposit   5,000.00    5,000.00   5,000.00    5,000.00    5,000.00
End        5,000.00  10,300.00  15,918.00  21,873.08  28,185.46

Future Value of an Annuity Due (FVad)

The Future Value of an Annuity Due is identical to an ordinary annuity except that each payment occurs at the beginning of a period rather than at the end. Since each payment occurs one period earlier, we can calculate the present value of an ordinary annuity and then multiply the result by (1 + i).

FVad = FVoa (1+i)

Where:
    FVad = Future Value of an Annuity Due
    FVoa = Future Value of an Ordinary Annuity
    i = Interest Rate Per Period

Example: What amount will accumulate  if we deposit $5,000 at the beginning of each year for the next 5 years?  Assume an interest of 6% compounded annually.

PV = 5,000 i = .06 n = 5

FVoa = 28,185.46 (1.06) = 29,876.59

Year                 1              2              3              4              5
Begin                0    5,300.00  10,918.00  16,873.08  23,185.46
Deposit   5,000.00    5,000.00   5,000.00    5,000.00    5,000.00
Interest     300.00       618.00      955.08    1,312.38    1,691.13
End        5,300.00   10,918.00 16,873.08  23,185.46  29,876.59

Categories: Economics & Finance
  1. No comments yet.
  1. No trackbacks yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: