**Question 2: Saving for Your Retirement**

Suppose your goal is to have a lump sum that you can withdraw when you retire. To accomplish this, you decided to contribute a portion of your paycheck in an annuity.

- Using the AIU Library or the Internet, read about what kind of expenses you will be faced with when you retire. Write a
**brief summary**of your research. - Based on your research, state the lump sum, in U.S. dollars, that you want to have when you retire. This is the future value of your investment; denote it by
.*F*

Future Value, F |
$ |

- State the time, in years, that you plan to contribute to your retirement account. Denote this by
.*t*

Time, t |

- Based on the first letter of your last name, choose the annual interest rate for your retirement account. Denote this by
, and*r*__you will convert this to its decimal form__. It does not necessarily have to be a whole number.

First letter of your last name |
Possible values for r |

A–F | 6.00%–7.99% |

G–L | 8.00%–9.99% |

M–R | 10.00%–11.99% |

S–Z | 12.00%–13.99% |

Annual interest rate in decimal form, r |

- From the table below, choose how many times per year you want to contribute to your retirement. Denote this by
, and this will also be your compounding period.*n*

Compounding Period |
n |

Yearly | 1 |

Semi-Annually | 2 |

Quarterly | 4 |

Monthly | 12 |

Compounding period, n |

- Calculate the interest rate per compounding period, which you will denote by
, by dividing the annual interest rate from #4 by the compounding period from #5, (i.e.,*i*

. Round your answer to ** 6 decimal places**.

Interest rate per compounding period, i |

7.Your contribution per period, which you will denote by ** C**, to this retirement account is calculated using the following formula:

Using the values that you have chosen for *F*, *i, n,* and *t*, calculate your contribution per period. __Use six decimal places for your intermediate calculations, and round your final answer to the nearest cent__.

**NOTE: Make sure to review exponents and the order of operations from College Math Chapter 1.**

- Calculate your
to this retirement account, which you will denote by__total contribution__, by using the formula TC = C x n x t.*TC*

- What can you say about the difference in value between your total contribution (
) and the lump sum (*TC*) that you will receive? Based on what you have learned in this unit, is there a term that is used for this difference?*F*

- Summarize the results of your calculations, and explain why it is important to prepare for your retirement.