Originally posted by @Chris May:
@Joshua S. @Gary Floring
I'll jump into the math later, but here's an analogy:
You take the bus to work. It's always a reliable 5 minutes each way. You plan on working there for 10 years. That means you have a total of 26,400 commute minutes in your future (5 minutes x 2 x 22 days in month x 12 months in year x 10 years).
You have a midlife crisis and switch jobs. The new job is in the same building. You tell everyone you saved 26,400 of commuting minutes by ditching that crummy job. Your friends say "but you're still commuting 10 minutes each day, you didn't save any time". To which you respond "but I decided I'm actually going to work one more year". By your math, you're only commuting another 5 x 2 x 22 x 10 = 2,200 minutes.
How about this scenario, using your analogy:
The guy originally signed a contract with his employer that he would work for 5,000 hours total [i.e., the "principle"]. The contract requires him to put in at least one hour per day, and at least five days a week, so he's on the hook to work at least 5 hours per week, or approx. 20 hrs. per month [i.e., his minimum "monthly payment"]. At that rate, it will take him almost 20 years to fulfill the contract. But the contract DOES allow him to work more if he wants to, as long as the total ["principle"] is 5,000 hrs. Note that his commute time is ONE HOUR each way, so he spends TWO hours of commute time [i.e., "interest"] to put ONE hour of time [i.e.., "principle"] into the contract each day.
So the guy says to himself, "At this rate, I'll be paying extra [i.e., "interest"] for my transportation costs back and forth, my daily lattes and snacks at the building, a new wardrobe and shoes every year, AND an extra TWENTY YEARS chained to a job that pays extremely well, but I hate the idea the idea of spending all that extra money [i.e., "interest"] for incidentals, the time commuting, AND time at the office. In fact, my commute time [i.e., "interest"] alone will be over 10,000 hours!!!"
Then he decides that he'll accelerate the contract in a much shorter time, like maybe 5 years instead. So he starts putting in many more hours per day and per week, thus accelerating his required total time [5,000 hrs. in "principle"] into a much shorter ["amortization"] schedule. Won't he thus "save" over 15,000 hours of [i.e., "interest"] time commuting, not to mention all the other incidental costs?