Question

Suppose that you are 25 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 seven and then stop the contributions. You will retire at age 70. You receive a 7% APR compounded monthly on your account. If you wanted an annual perpetuity of $200000, how much per month should you have originally computed?

Group of answer choices

$730-$735

> $735

< $720

$720-$725

$725-$730

Answer 1

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

Value at 67 years = Value at retirement(@ 70 years) / (1 + r)ⁿ

= $200,000 / [1 + (0.07/12)]^(3*12)

= $200,000 / 1.2329 = $162,215.7915

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

$162,215.79 = P + P * [{1 - (1 + 0.07/12)^{-[{(67-25)*12}-1]}} / (0.07/12)]

$162,215.79 = P + P * [0.9464 / 0.0058]

$162,215.79 = P + P * [162.2348]

$162,215.79 = P * [163.2348]

P = $162,215.79 / 163.2348 = $993.76