if you want to save $5,000 before buying your first new car, and you have $3,000 right now to invest at 3% interest compounded monthly, how long will you have to wait?

Guest Apr 22, 2017

#1**+1 **

5000 = 3000(1 + .03)^(12 * t) where t is the time in years

Divide both sides by 3000

5/3 = (1 + .03/12)^(12 * t) take the log of both sides

log (5/3) log (1+ .03/12)^(12*t) and we can write

log (5/3) = (12 * t) log (1+ .03/12)

log (5/3) = 12 * log (1+ .03/12) * t divide both sides by 12*log (1.03/12)

log (5/3) / [ 12 * log (1+ .03/12) ] = t ≈ 17 years

CPhill
Apr 22, 2017