You started your first job after graduating from college. Your company offers a retirement plan for which the company contributes 50% of what you contribute each year. You expect to contribute $4,000 per year from your salary. You decide to invest the contributions in assets that you expect to earn 8% per year. If you plan to retire in 35 years, how big will you expect that retirement account to be?
A) $689,267.21
B) $823,147.29
C) $1,033,900.82
D) $1,308,427.41

Question

Quizplus · Accepted Answer

Using the formula for future value of an ordinary annuity:

FV = PMT [(1 + r)^n - 1]/r

where:
PMT = $4,000 (annual contribution)
r = 8% (annual interest rate)
n = 35 (number of years)

Calculating the future value of the annuity, we get:

FV = $4,000 [(1 + 0.08)^35 - 1]/0.08
FV = $4,000 [12.9774]/0.08
FV = $647,870

Since the company contributes 50% of what you contribute each year, the total contribution each year is $6,000 (your $4,000 plus $2,000 from the company). Therefore, the total future value of the account would be:

Total FV = $647,870 x 2
Total FV = $1,295,740

The closest option is C: $1,033,900.82, which is slightly lower than the calculated value due to compounding of interest.

You Started Your First Job After Graduating from College