Question

Leif started making contributions to a Traditional IRA when he got his first job, at age 32. His contributions averaged $3,200 annually. Leif was in the 20% tax bracket during his working years, when he continued to make these annual contributions. The average annual rate of return on the account was 6.8%. Upon retirement at age 69, Leif stopped working and making IRA contributions. Instead, he started living on withdrawals from the retirement account. At this point, Leif dropped into the 10% tax bracket. Factoring in taxes, what is the effective value of Leif’s Traditional IRA at retirement?

Answer 1

Assume annual compounding

Answers:
$440,728.02

$305,314.21

$483.080.97

$391,758.24

Answer 2

69-32 = 37 ==> 3200 * 1.068^37
69-33 = 36 ==> 3200 * 1.068^36
69-34 = 35 ==> 3200 * 1.068^35
69-35 = 34 ==> 3200 * 1.068^34
etc.
69-67 = 2 ==> 3200 * 1.068^2
69-68 = 1 ==> 3200 * 1.068^1

Where is this leading?

Answer 3

69-69=0 ==> 3200 * 1.068^0

Answer 4

Okay, now add them all up?

3200 * 1.068^37 + 3200 * 1.068^36 + ... + 3200 * 1.068^0

3200 * (1.068^37 + 1.068^36 + ... + 1.068^0)

\(3200\cdot \dfrac{1.068^{38} - 1.068^{1}}{1.068 - 1}\)

Now what>

Answer 5

Thank you!