Question

Suppose that you are 21 years old, and making retirement plans. You are starting to contribute monthly to your retirement account at the beginning of each month. You intend to do so until the age of sixty five and then stop the contributions. You will retire at age 67. You receive a 6.5% APR compounded monthly on your account. If you wanted an annual perpetuity of $165000, how much per month should you have originally computed?

Group of answer choices

$700-$705

> $715

$710-$715                                                      

$705-$710

< $700

Answer 1

First, we need to find the value at the 67 years

Value at 65 years = Value at retirement(@ 67 years) / (1 + r)ⁿ

= $165,000 / [1 + (0.065/12)]^(2*12)

= $165,000 / 1.1384 = $144,936.58

Future Value of Annuity Due = Monthly Deposit + Monthly Deposit * [{1 - (1 + r)^-n} / r]

$144,936.58 = P + P * [{1 - (1 + 0.065/12)^{-[{(65-21)*12}-1]}} / (0.065/12)]

$144,936.58 = P + P * [0.9420 / 0.0054]

$144,936.58 = P + P * [173.9031]

$144,936.58 = P * [174.9031]

P = $144,936.58 / 163.2348 = $828.67