Answer
See an explanation
Work Step by Step
$A(t)=P(1+\frac{r}{n})^{nt},$
$P=10000, n=2, t=18, r=0.04$
$A(18)=10000(1+0.02)^{2\times 18},$
$=10000(1.02)^{36},$
$=20398.87,$
The bond will be worth at maturity $20398.87,$
When the bond doubles in value
$20000=10000(1.02)^{2t},$
$2=(1.02)^{2t},$
$\log2=2t\log(1.02),$
$\frac{\log2}{2\log(1.02)}=t,$
$t=17.5$
Thus, it will take $17.5$ years to double in value.
