Answer:
$9,252.23 ≈ a. $9,252
Explanation:
Jordan will retire at 67 and expects to live 30 more years. Be believes that he will need approximately $82,000 (in current dollars) per year to live while he is retired. his social security benefits are $30,000 (in current dollars) per year, so that means that he needs to cover the remaining $52,000. In order to calculate this, I will assume that Jordan receives his first distribution on his 67th birthday (annuity due) and each distribution is made on an annual basis and received on the subsequent birthdays until he turns 96 (30th distribution).
The $52,000 that Jordan expects to need once he retires must be adjusted to inflation (3%). In 12 years they will equal $52,000 x (1 + 3%)¹² = $74,139.57
Using an excel spreadsheet, I calculated the present value of Jordan's 30 distributions using a 9% discount rate = $1,100,465.22
Jordan currently has $325,000 in his retirement account and in 12 years (age 67), his account will be worth $325,000 x (1 + 9%)¹² = $914,116.05
this means that Jordan will be $1,100,465.22 - $914,116.05 = $186,349.17 short
using the future value of an annuity formula, we can calculate the annual contribution:
annual contribution = future value / annuity factor
- future value = $186,349.17
- FV annuity factor, 9%, 12 periods = 20.141
annual contribution = $186,349.17 / 20.141 = $9,252.23 ≈ $9,252
