Answer:
$2.1 million
Explanation:
Colin will retire at 67 and expects to live 28 more years. Be believes that he will need approximately $112,500 (in current dollars) per year to live while he is retired. His social security benefits are $30,000 + $20,000 in a government sponsored annuity (in current dollars) per year, so that means that he needs to cover the remaining $62,500. In order to calculate this, I will assume that Colin 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 94 (28th distribution).
The $62,500 that Jordan expects to need once he retires must be adjusted to inflation (3%). In 27 years they will equal $62,500 x (1 + 3%)²⁷ = $138,830.56
Using an excel spreadsheet, I calculated the present value of Colin's 28 distributions using an 8% discount rate = $2,064,637.04
, which we can round up to $2.1 million
Colin currently has $200,000 in his retirement account and in 27 years (age 67), his account will be worth $200,000 x (1 + 8%)²⁷ = $1,597,612.29
this means that Colin will be $2,064,637.04 - $1,597,612.29 = $467,024.75 short
using the future value of an annuity formula, we can calculate the annual contribution:
annual contribution = future value / annuity factor
- future value = $467,024.75
- FV annuity factor, 8%, 27 periods = 87.35077
annual contribution = $467,024.75 / 87.35077 = $5,346.54
