Given the word problem, we can deduce the following information:
Principal amount = $4739
Future amount = $5336
Interest = 5.1 % =0.051
To determine the time to accumulate the $5336, we use the compound interest formula:
A=Future amount=$5336
P=Present amount=$4739
r=interest rate = 0.051
n=number of compounding periods =12
t=time in years
We also note that the number of compounding periods must be 12 since the investment is compounded monthly.
We plug in what we know:
![\begin{gathered} A=P(1+(r)/(n))^(nt) \\ 5336=4739(1+(0.051)/(12))^(12t) \\ Simplify\text{ and rearrange} \\ 5336=4739((12.051)/(12))^(12t) \\ 12t=(\ln(5336)/(4739))/(\ln(12.051)/(12)) \\ t=\frac{\operatorname{\ln}(5,336)/(4,739)}{12\operatorname{\ln}(12.051)/(12)} \\ Calculate \\ t=2.33 \end{gathered}]()
Therefore, the answer is 2.33 years.