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:

Ia_{n|i} = | Arithmetic Payment x (ä_{n|i} - nv^{n}) |

| i |

__Calculate d__d = 0.074

__Calculate Present Value of Annuity Factor (PVA) given i = 0.08, n = 4, and v = 0.93__ä_{4|0.08} = | (1 - 0.93^{4}) |

| 0.074 |

ä_{4|0.08} = | (1 - 0.45) |

| 0.074 |

ä

_{4|0.08} =

**3.5771**__Now Calculate the Present Value of an Increasing Arithmetic Annuity:__Ia_{4|0.08} = | Arithmetic Payment x (ä_{4|0.08} - nv^{n}) |

| i |

Ia_{4|0.08} = | 100 x (3.5771 - 4(0.93)^{4}) |

| 0.08 |

Ia_{4|0.08} = | 100 x (3.5771 - 4(0.45)) |

| 0.08 |

Ia_{4|0.08} = | 100 x (3.5771 - 2.8) |

| 0.08 |

Ia_{4|0.08} = | 100 x 0.19 |

| 0.08 |

Ia

_{4|0.08} =

**773**__Calculate the Accumulated Value of an Increasing Arithmetic Annuity:__Is_{n|i} = | Arithmetic Payment x (s_{n|i} - n) |

| i |

s_{n|i} = | (1 + i)^{n} - 1 |

| d |

s_{n|i} = | (1 + 0.08)^{4} - 1 |

| 0.074 |

s_{n|i} = | 1.08^{4} - 1 |

| 0.074 |

s_{n|i} = | 1.36048896 - 1 |

| 0.074 |

s_{4|0.08} = 4.86660096

__Calculate AV given i = 0.08, n = 4__Is_{n|i} = | 1000 x (s_{n|i} - n) |

| 0.08 |

Is_{n|i} = | 1000 x (4.86660096 - 4) |

| 0.08 |

Is_{n|i} = | 1000 x (0.86660096) |

| 0.08 |

Is

_{n|i} =

**10832.512**