The function growingannuity calculates the present value at period=0, of an annuity of nperiods payments, starting at period=1 with a payment of cash. The payments increase at a rate growth per period.

Since growingannuity used to be part of the (now deprecated) finance package, for compatibility with older worksheets, this command can also be called using finance[growingannuity]. However, it is recommended that you use the superseding package name, Finance, instead: Finance[growingannuity].

$\mathrm{with}\left(\mathrm{Finance}\right)\:$

$\mathrm{growingannuity}\left(100\,0.11\,0.03\,5\right)$

$390.0340764$

$\mathrm{cf}≔\left[100\,100\cdot 1.03\,100{1.03}^2\,100{1.03}^3\,100{1.03}^4\right]$

$\mathrm{cf}≔\left[100\,103.00\,106.0900\,109.272700\,112.5508810\right]$

$i≔'i'\:$

$\mathrm{cf}≔\left[\mathrm{seq}\left(\mathrm{futurevalue}\left(100\,0.03\,i\right)\,i=0..4\right)\right]$

$\mathrm{cf}≔\left[100.0\,103.00\,106.0900\,109.272700\,112.5508810\right]$

$\mathrm{cashflows}\left(\mathrm{cf}\,0.11\right)$

$390.0340762$

$\mathrm{part1}≔\mathrm{growingannuity}\left(1.12\,0.12\,0.12\,6\right)$

$\mathrm{part1}≔6.000000000$

$\mathrm{div\_6}≔\mathrm{futurevalue}\left(1.12\,0.12\,5\right)$

$\mathrm{div\_6}≔1.973822685$

$\mathrm{div\_7}≔\mathrm{futurevalue}\left(\mathrm{div\_6}\,0.08\,1\right)$

$\mathrm{div\_7}≔2.131728500$

$\mathrm{part2\_6}≔\mathrm{growingperpetuity}\left(\mathrm{div\_7}\,0.12\,0.08\right)$

$\mathrm{part2\_6}≔53.29321250$

$\mathrm{part2}≔\mathrm{presentvalue}\left(\mathrm{part2\_6}\,0.12\,6\right)$

$\mathrm{part2}≔27.00000000$

$\mathrm{part1}+\mathrm{part2}$

$33.00000000$

The Finance[growingannuity] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.