Future Value of Annuity

Future Value of Annuity:

• It is a special case of multiple payments
• The symbol of cash flow is C or Pmt.

Exactly at 0 year, cash flow is 0. From 0-1, 1-2 and 2-3 the cash flows are C.

Now let us calculate future value:

In 0 year, FV = 0.

In period 1, FV = C*(1+r) ^{^2}

In period 2, FV = C*(1+r)

In period 3, FV = C

FV of an annuity: Formula

FV = C (1+r) ^{^2} + C (1+r) + C

      = C [(1+r) ^{^2} + (1+r) + 1]

  FV_n    = C [(1+r) ^^n-1 + (1+r) ^^n-2+…….. + 1]

Note: In Excel, the formula is =FV (rate, nper, pmt, [ pv ], [type]). Put your yearly payment in pmt. Put nothing on [PV] and [type]. See Example 1.

Another  formula is =pmt (rate, nper, pv, [ fv ], [type]). Put 0 in pv. See Example 2.

FV of Annuity: Example 1

What will be the value of your portfolio at retirement if you deposit $10,000 every year in a pension fund. You plan to retire in a 40 years and expect to earn 8% on your portfolio.

Solution:

let us use excel calculator to solve the problem:

                                       = FV (rate,nper,pmt,[PV],[type])

                                       = FV (0.08,40,10000) dont put anything on PV and type. and press enter

                                       = $2,590,565

Example II

Suppose you want to guarantee yourself $500,000 when you retire 25 years from now. How much must you invest each year, starting at the end of this year, if the interest rate is 8%?

Solution:

In Excel,

                  = pmt (rate,nper,pv,[fv],[type])

                  = pmt (0.08,25,0,500000)

                  = $6,839

Click the download button to download the formula: