Question

Find the time required for ​$2000 to be equal to ​$25 comma 000 when deposited at 6​% compounded monthly.

Answer 1

A = P*(1 +r/n)^(nt)
25000 = 2000*(1 +.06/12)^(12t)
12.5 = 1.005^(12t) . . . . . . . . . . . . . . divide by 2000, simplify
log(12.5) = 12t*log(1.005) . . . . . . .. take logs
t = log(12.5)/(12*log(1.005)) . . . . . . solve for t
t ≈ 42.2

It will take about 42 years and 2.4 months for $2,000 to become $25,000 at that interest rate.