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?
+128406 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
