I recently signed up for a PNC checking account through a promotion that will reward me $200 for jumping through a few hoops and I had an interesting thought after clicking the apply button. Why am I doing this? Probably a question one should answer before going ahead with anything, but I think I’ll be okay in this instance. A free $200 is a free $200 right? The entire process of opening the account, completing the tasks, and closing the account won’t take me more than an hour, probably closer to 30 minutes. That means I’m effectively making up to $400/hour! Well that’s great and all, but the real value I’m getting out of it is a little harder to measure. After some thought, I’ve developed a fairly effective way to measure the value of a bank bonus like this in the context of my greater financial goal, financial independence. I simplified the math by calculating for $100, but it can be adjusted to calculate the value of any amount of extra money. Follow along with me and you might never look at a cash signup bonus the same way again.

## The Value of $100 Depends On Your Goals

When we talk about value, the money itself is just a middleman between the effort put in to earn it and the things you buy with it. Everyone uses their money differently, so what you actually spend the $100 on is going to impact the value. Going out to a nice dinner, buying a new gadget, or filling up your gas tank are some of the options you can use the $100 for, but it’s fairly difficult to measure exactly how much “value” you got out of the purchase. Value in this case being the utility, happiness, pleasure, or any other benefit you gained from the transaction.

The thing I plan to spend my $100 on is a lot easier to measure, **Freedom**. More specifically, freedom from the hours I spend at work to fund the expenses in the rest of my life (aka Financial Independence). How much does that freedom cost? I’m a fairly strong believer in the 4% rule, so that freedom costs exactly 25 times my yearly expenses.

Knowing that I have an extra $100, we can measure exactly how much freedom that will buy me. The result being the exact number of hours I’ll no longer have to work in order to become financially independent. If we think of all the hours I’ll work between now and my FI date, we can slowly start knocking off the hours at the very end by investing more today. In order to determine how many hours the extra $100 will save you, we need to calculate two numbers, Real Hourly Wage and Years to FI.

## Calculating Real Hourly Wage

This one is fairly straightforward and depends on how many hours you work and how much you earn per year.

When calculating the number of hours worked, I prefer to subtract out all the holidays, vacations, and other times I wouldn’t actually be working such as sick days. This allows me to focus entirely on the number of hours I spend in the office during a given year.

For example, let’s start with a typical 5 days a week for a total of 260 days per year. Then we can subtract out 6 holidays off in a year, 3 weeks of vacation, and 4 sick days. That gives us a total number of actual days worked of 235 days (260 – 6 – 15 – 4). We can multiply that by the typical number of hours worked of 8 to get an approximate number of hours worked in a year of 1880.

Now that we know how many hours are actually worked per year, we need to determine the actual amount of money you make in a given year. We should look at the net income for this, so we can subtract out any taxes that are paid from your gross income. Don’t forget to include any 401k contributions or similar that come out of the paycheck. We want to account for all of the money that you either have access to immediately or will have access to in the future.

Once we have both the total numbers of hours worked in a year and the net yearly income, we can calculate Real Hourly Wage:

**Real Hourly Wage = Yearly Net Income / Yearly Hours Worked**

## Calculating Years to Financial Independence

We could naively just divide $100 by the Real Hourly Wage to calculate how many hours it would buy today, but your FI date probably isn’t today! The further away from FI you are, the more hours of freedom that $100 will be able to buy you. The $100 now will grow to be worth more than $100 by the time you actually start using it, so we need to factor in compounding. The only thing necessary at that point is determining how many years until you will reach FI. Not the simplest of tasks, but there’s an easy way to ballpark it.

If we were looking at a traditional retirement of 65 years old, you could simply subtract your age from 65, but we know you can do a lot better than that, especially if you start early. Your exact number will depend mostly on what you’re starting with and your savings rate. An awesome tool for approximating your FI date is the Networthify “When Can I Retire?” calculator. Simply plug in your current investments and your annual income/expenses to get a straightforward number of years to retirement.

## Putting It All Together

Once we have a Real Hourly Wage and a number of Years to FI, we just need a value for expected growth. This entire calculation will be with real dollars, so take inflation out of the growth number. Most calculations use a conservative 5-6% for this growth number. Now we just plug the 3 numbers in below to determine how many hours of freedom can be purchased with that extra $100:

Hours of Freedom = ($100 * ((1 + Expected Growth %) ^ Years to FI)) / Real Hourly Wage

## My Hours Of Freedom Calculation

I chose $100 because it’s easy to adjust to any number once Hours of Freedom is calculated, but it’s also possible to simply change the number in the above formula to any amount of money. First let’s calculate how many hours of freedom $100 buys me, then scale it up for the $200 bank bonus I mentioned initially.

**My Real Hourly Rate = $45
My Approximate Years to FI = 13**

Expected Growth = 6%

Expected Growth = 6%

Hours of Freedom = ($100 * ((1 + 0.06) ^ 13)) / $45

Hours of Freedom = (100 * (1.06 ^ 13)) / 45

Hours of Freedom = (100 * 2.133) / 45

Hours of Freedom = 213.3 / 45

**Hours of Freedom = 4.74**

That means for every extra $100 I can come up with now and invest, I’ll save myself almost 5 hours of working at my job! If I value my hours now at the same level I will value them once FI, that effectively means if I can earn $100 with less than 5 hours of work, it’s probably worth doing. Keep in mind there are definite diminishing returns and opportunity costs when pursuing extra income. Be careful not to overwork yourself or miss other life opportunities simply to save yourself a little bit of time in the office in the future.

If we want to scale this to the $200 bank bonus that kicked off my line of thinking here, we first need to see what the “$200” bank bonus is actually worth. As bank bonuses are taxed like income, I first need to subtract out the taxes. I’m not sure what my marginal tax rate will be this year, so let’s call it 25% for a final profit from the bank bonus of $150. Now that I know an extra $100 buys me 4.74 hours of freedom, I simply need to multiply by 1.5 ($150 / $100) to find out how much $150 buys me. That number comes out to 7.11 hours, so a little less than a full 8 hour day.

For 30 minutes of my time, I can save myself 7 hours of being in the office in the not to distant future? That seems like a worthy trade and helps justify the extra effort spent pursuing a few hundred extra dollars here and there.

## Small Warning

While this calculation is accurate for smaller amounts of money such as hundreds or even thousands, the actual number of hours saved has diminishing returns. The reason for this is that every time you buy yourself an hour of freedom, your money has 1 less hour to compound before you reach FI. On the scale of hours and days this difference will be minuscule, but plugging in a big number relative to your FI number will throw off the final result.

## How Much Is An Extra $100 Worth To You?

There are a lot of different ways to generate an extra $100 including signup bonuses, cutting down your regular expenses, or finding a small side-gig on the weekends. While I choose to try buying freedom with any extra money that comes my way, I know other people handle “bonuses” differently. Do you invest every extra penny that comes your way, or do you treat yourself when some unexpected money comes in? If you’re not measuring financial independence progress like myself, how do you determine if going out of your way to make an extra $100 is worth your time? Let me know how you value an extra $100, I’m curious to see other people’s thought process when it comes to small opportunities like bank bonuses. For me, I’ll happily keep pursuing side opportunities to slowly buy back hours of my life at a reduced rate. For some reason, the money I earn outside of work seems much more satisfying than my regular paycheck, even if it’s small in comparison.

Why not go for the $400?

The direct deposit for my job is easy to change, but I don’t have $5,000 in a month to send to PNC that isn’t already committed to other bonuses (like Santander). My choice was to either get creative and try making an ACH transfer trigger the bonus or just take the smaller bonus and save myself the effort. The smaller effort won out.

Sometimes I get caught up in a mindset of do it optimally or don’t do it at all, but I try to remind myself that taking the middle road for some of the benefit is often better than ignoring the opportunity completely.

That’s why I settled for the $200 bonus in this case, but the post is more about the value of ANY extra money and not any particular bonus.

Great post! One note — you should probably discount inflation (3%), which changes the compounding a LOT.

Thanks!

I actually mentioned in the middle: “This entire calculation will be with real dollars, so take inflation out of the growth number.”

By keeping all of the numbers in present day dollars, we don’t have to worry about inflation to get the correct result in hours. That is also why the conservative growth number is in the 5-6% range instead of a higher number that includes inflation. The real return of the stock market over the past 100+ years has been ~7% AFTER inflation! If you were to subtract out your 3% inflation again on top of the 5-6% number I suggested, it would no longer be close to historical returns and will yield less accurate results.

When I earn bonuses like these, I tuck them away in investments or savings. If I never expected it to be there, it’s a lot easier to pretend it’s not there. The money pile just keeps growing and growing. 🙂

Nice! I love this kind of math-related post! I’m a number nerd and an engineering undergrad, so I can get way into this way of thinking. Reminds of the Mr. Money Mustache Article on why $10 is still $10.

Also, interesting take “real hourly wage” vs. the Viki Robin approach. I find your method easier to calculate and wrap my mind around.