### Author Topic: Calculating hypothetical "catch up" retirement  (Read 1945 times)

#### monstermonster

• Magnum Stache
• Posts: 4291
• Age: 35
• Location: The People's Republic of Portland (Oregon)
##### Calculating hypothetical "catch up" retirement
« on: May 15, 2015, 10:38:06 AM »
I'm trying to solve a non-urgent question for my friend, and I'm looking for some help on a hypothetical math problem.

He's trying to figure out how much he is "behind" or "ahead" of a "typical" retirement savings track given that he was in start-up/freelance mode for a long time, was not contributing to retirement, and then at age 28 his startup got acquired and he put a huge chunk of money in his 401K and then started contributing regularly (He is now 30.) He's trying to figure out if he put enough in to "make up" for the retirement he would have had if he had done the "normal" job-with-benefits thing. This isn't actually that important, but is a fun exercise.

I'm assuming he would have had a starting engineer salary of about \$60,000.
Let's say he would have contributed 12% to a Traditional 401K from ages 24-28 (\$7200/year), and the 401K compounds monthly. So a simple compound interest calculation assuming an 8% rate of return would be:

Lost value = 7200 (1 + 0.05 / 12) ^ 12(8)

Here's my questions:
1) Is there a way to easily figure out compound interest for a historical time period for a fund? Like could I look at what a vanguard lifecycle fund did from 2009-2013 to figure out theoretical return he would have gotten on  \$7200/year? Especially given how the market was pretty bleak during that time...
2) Do you see any flaws with my logic? At the moment I have him at needing to make a \$34,035.35 catch-up contribution (luckily his catchup was actually twice that). Does that make sense?

#### MDM

• Senior Mustachian
• Posts: 11185
##### Re: Calculating hypothetical "catch up" retirement
« Reply #1 on: May 15, 2015, 11:14:19 AM »
I'm trying to solve a non-urgent question for my friend, and I'm looking for some help on a hypothetical math problem.

He's trying to figure out how much he is "behind" or "ahead" of a "typical" retirement savings track given that he was in start-up/freelance mode for a long time, was not contributing to retirement, and then at age 28 his startup got acquired and he put a huge chunk of money in his 401K and then started contributing regularly (He is now 30.) He's trying to figure out if he put enough in to "make up" for the retirement he would have had if he had done the "normal" job-with-benefits thing. This isn't actually that important, but is a fun exercise.

I'm assuming he would have had a starting engineer salary of about \$60,000.
Let's say he would have contributed 12% to a Traditional 401K from ages 24-28 (\$7200/year), and the 401K compounds monthly. So a simple compound interest calculation assuming an 8% rate of return would be:

Lost value = 7200 (1 + 0.05 / 12) ^ 12(8)

Here's my questions:
1) Is there a way to easily figure out compound interest for a historical time period for a fund? Like could I look at what a vanguard lifecycle fund did from 2009-2013 to figure out theoretical return he would have gotten on  \$7200/year? Especially given how the market was pretty bleak during that time...
2) Do you see any flaws with my logic? At the moment I have him at needing to make a \$34,035.35 catch-up contribution (luckily his catchup was actually twice that). Does that make sense?
1) You could look at the Morningstar "growth of \$10K" charts.  E.g., http://www.morningstar.com/funds/XNAS/VTHRX/quote.html: for the 4.5 years from 6/30/2009 (\$8,650) through 12/31/2013 (\$16,153) the CAGR = (16153/8650)^(1/4.5) - 1 = 14.89%

2) Assume the contributions would have been \$600/mo, made at the end of the month, done for 48 months.  See http://en.wikipedia.org/wiki/Time_value_of_money#Future_value_of_an_annuity.
For an 8% CAGR, the formula is \$600 * (1+.08/12)^48 - 1) / (.08/12) = \$33,810
For 14.89% the result is \$39,046.