Challenge for you...

You purchase a new vehicle for 12, 500 dollars. This particular vehicle depreciates at a rate of 1.2%. How many months will it take for your new vehicle to be worth LESS THAN $3,000?

Is it 1.2% per month? If yes, then the car will depreciate to just under $3,000 in 120 months or 10 years. Use: 12,500/ (1.012)^n=< $3,000. Solve for n=120.

If it depreciates every month at 1.2%...then each successive month, it must be worth only   98.8%  = .988  of what it was the prior month......so we have

3000  =  12,500 (.988)^m        divide both sides by 12500

30/125  = (.988)^m     take the log of both sides

log (30/ 125)  = log .988 ^m      and we can write

log(30/ 125)   = m log .988      divide both sides by log.988

log(30 / 125)  / log(.988) = m  = about 118.2 months.....actually....  m > 118.2 months since,at any time after this, it will be worth less than $3000

The car depreciates by 1/1.012=0.98814229, then:

Log(3,000/12,500)=nLog(0.98814229)

-0.61978875=n X -0.005180513

n=119.64 months. Anything > this will depreciate the car just under $3,000. In fact, at 120 months will be worth=$2,987.09, exactly.