Question

How much time will be needed for $38,000 to grow to $40,948.14 if deposited at 3% compunded quarterly?​

Answer 1

log (1.0406039474) = log ((1.01)0.04t)

log (1.0406039474) = 0.04t * log (1.01) - Power Rule

log (1.0406)/log(1.01) = 0.04t

log1.01(1.0406) = 0.04t - change of base formula

t = log1.01(1.0406) / 0.04

t = 99.99031

I'd round this up to 100 years.