To solve this problem, we can use the compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where A represents the accrued value, P represents the invested value, r represents the interest(in decimals), n represents the amount of times the interest is compounded per unit 't' and t represents the time.
Since the unit of the time 't' is years, and the interest is compounded yearly, n = 1.
To write a percentage as a decimal, we just have to divide the percentage value by 100.
[tex]3.6\%=0.036[/tex]To find the amount of time t, we just have to subtract the year the money was invested from the year we want to know the money accrued.
[tex]t=2029-2011=18[/tex]Then, using those values on the formula, we have
[tex]\begin{gathered} A=13,000(1+0.036)^6 \\ A=16073.1828298\ldots\approx16073.18 \end{gathered}[/tex]The accrued value in the year 2029 will be $16,073.18.
