Question

Colin is 40 years old and wants to retire in 27 years. His family has a history of living well into their 90s. Therefore, he estimates that he will live to age 95. He currently has a salary of $150,000 and expects that he will need about 75% of that amount annually if he were retired. He can earn 8 percent from his portfolio and expects inflation to continue at 3 percent. Some years ago, he worked for the government and expects to receive an annuity that will pay him $20,000 in today’s dollars per year beginning at age 67. The annuity includes a cost of living adjustment, which is equal to inflation. Colin currently has $200,000 invested for his retirement. His Social Security benefit in today’s dollars is $30,000 per year at normal age retirement of age 67. How much does he need to accumulate at age 67 exclusive of his pension and Social Security benefits? Group of answer choices $2.1 million. $2.2 million. $2.8 million. $2.9 million.

Answer 1

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