Answer
$t=1.833~years\approx669~days$
Work Step by Step
$A=P(1+\frac{r}{n})^{nt}$
$r=5.2$% $=0.052$
$P=100,00$
$A=100,000+10,000=110,000$
$110,000=100,000(1+\frac{0.052}{365})^{365t}$
$1.1=(1+\frac{0.052}{365})^{365t}$
$\log1.1=\log(1+\frac{0.052}{365})^{365t}$
$\log1.1=365t[\log(1+\frac{0.052}{365})]$
$t=\frac{\log1.1}{365\log(1+\frac{0.052}{365})}=1.833$