Well...that depends upon what amount we're starting with....
Notice that the worth of the capital at the end of each successive year is only 95.73% of the ending amount in the prior year....
Let's see how long it will take one dollar to be worth less than a penny.....so we have...
.01 = 1(.9573)t = (.9573)t
Take the log of both sides
log (.01) = t log(.9573)
log(.01)/(log.9573) = t ≈ 105.53 yrs ≈ 106 years
Somewhat surprising, huh??
Now, less suppose that we started with 100 dollars...so we have
.01 = 100(.9573)t divide both sides by 100
.0001 = (.9573)t take the log of both sides
log(.0001)/(log.9573) = t ≈ 212 years
Here's the graph of the situation if we start with $1
Also notice, that, theoretically, we're never "broke" because an exponential graph is never equal to 0 !!!
