ANSWER :
The answer is 20.3971 years
EXPLANATION :
The compounding interest formula is :
where :
FV = future value ($6800)
PV = present value ($2900)
r = rate of interest (4.2% or 0.042)
n = number of compounding in a year (4 : compounded quarterly)
t = time in years
Using the formula above :
Solve for t :
![\begin{gathered} (6800)/(2900)=(1.0105)^(4t) \\ \text{ take ln of both sides :} \\ \ln((6800)/(2900))=\ln(1.0105)^(4t) \\ \operatorname{\ln}((6800)/(2900))=4t\operatorname{\ln}(1.0105) \\ 4t=(\ln((6800)/(2900)))/(\ln(1.0105)) \\ t=(\ln((6800)/(2900)))/(4\ln(1.0105)) \\ t=20.3971 \end{gathered}]()