Arithmetic Annuity Calculator

 First Payment Progression Payment N Interest Rate Increasing Decreasing
or

Given an interest rate of 8% and a first payment amount of 1000 arithmetically increasing by 100 for 4 periods, calculate the Present Value (PV) and Accumulated Value (AV) of an Increasing Arithmetic Annuity Immediate:

 Ian|i  = Arithmetic Payment x (än|i - nvn) i

Calculate d
 d  = i 1 + i

 d  = 0.08 1 + 0.08

 d  = 0.08 1.08

d = 0.074074074074074

Calculate Present Value of Annuity Factor (PVA) given i = 0.08, n = 4, and v = 0.92592592592593
 ä4|0.08  = (1 - 0.925925925925934) 0.074074074074074

 ä4|0.08  = (1 - 0.73502985279645) 0.074074074074074

 ä4|0.08  = 0.26497 0.0740741

ä4|0.08 = 3.5771

Now Calculate the Present Value of an Increasing Arithmetic Annuity:
 Ia4|0.08  = Arithmetic Payment x (ä4|0.08 - nvn) i

 Ia4|0.08  = 100 x (3.5771 - 4(0.92592592592593)4) 0.08

 Ia4|0.08  = 100 x (3.5771 - 4(0.73502985279645)) 0.08

 Ia4|0.08  = 100 x (3.5771 - 2.9401194111858) 0.08

 Ia4|0.08  = 100 x 0.63698058881419 0.08

 Ia4|0.08  = 63.6981 0.08

Ia4|0.08 = 796.22573601773

Calculate the Accumulated Value of an Increasing Arithmetic Annuity:
 Isn|i  = Arithmetic Payment x (sn|i - n) i

 sn|i  = (1 + i)n - 1 d

 sn|i  = (1 + 0.08)4 - 1 0.074074074074074

 sn|i  = 1.084 - 1 0.074074074074074

 sn|i  = 1.36048896 - 1 0.074074074074074

 sn|i  = 0.360489 0.0740741

s4|0.08 = 4.86660096

Calculate AV given i = 0.08, n = 4
 Isn|i  = 1000 x (sn|i - n) 0.08

 Isn|i  = 1000 x (4.86660096 - 4) 0.08

 Isn|i  = 1000 x (0.86660096) 0.08

 Isn|i  = 866.601 0.08

Isn|i = 10832.512