Question

5. 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?

   1. $2.1 million.

   2. $2.2 million.

   3. $2.8 million.

   4. $2.9 million.

Answer 1

b. $2.2 million.

The pension can be treated in the same manner as Social Security because it occurs at the same time and includes
a COLA. Choice a is calculated as an ordinary annuity. Choice C is calculated without the pension and as an ordinary
annuity. Choice d is calculated without the pension.