# John wants to make a deposit on January 1, 2016, to be able to withdraw $1,200 at the beginning...

## Question:

John wants to make a deposit on January 1, 2016, to be able to withdraw $1,200 at the beginning of each year starting January 1, 2020, for four years. The interest rate is 6 percent. What is the amount of the deposit that John needs to make on January 1, 2016?

## Annuity:

After retirement, when we will not have any active income stream, we can create an annuity of periodic cash flows to support our living by accumulating the amount while we still are working.

## Answer and Explanation: 1

John wants an annuity with cash flows of $1,200 starting from January 1, 2020, for four years.

John should deposit the amount equal to the present value of the annuity in the account earning a 6% interest rate.

**Computation of present value of annuity on January 1, 2020**

Date | Amount | Present value on Jan 1, 2020 |
---|---|---|

January 1, 2020 | $1,200 | $1,200.00 |

January 1, 2021 | $1,200 | $1,200 / 1.06 = $1,132.08 |

January 1, 2022 | $1,200 | $1,200 / 1.06^2 = $1,068.00 |

January 1, 2023 | $1,200 | $1,200 / 1.06^3 = $1,007.54 |

Total | $4,407.62 |

To arrive at the present value on January 1, 2016, we will further discount for 4 years.

{eq}\text{Amount to be deposited} = \dfrac{\$4,407.62}{1.06^4} {/eq}

{eq}\text{Amount to be deposited} = \$3,491.25 {/eq}

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Chapter 2 / Lesson 7An annuity is a fixed amount of income paid at regular intervals, such as monthly or quarterly. Learn the definition and formula for annuity, review examples of annuities, and understand how to determine the value of annuities.