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 = 0.074

Calculate Present Value of Annuity Factor (PVA) given i = 0.08, n = 4, and v = 0.93
ä4|0.08 =(1 - 0.934)
0.074

ä4|0.08 =(1 - 0.45)
0.074

ä4|0.08 =0.55
0.074

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(0.93)4)
0.08

Ia4|0.08 =100 x (3.5771 - 4(0.45))
0.08

Ia4|0.08 =100 x (3.5771 - 2.8)
0.08

Ia4|0.08 =100 x 0.19
0.08

Ia4|0.08 =63.
0.08

Ia4|0.08 = 773

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
0.074

sn|i =1.084 - 1
0.074

sn|i =1.36048896 - 1
0.074

sn|i =0.36048896
0.074

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 =866.60096
0.08

Isn|i = 10832.512