Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 405: 92

$t=2.344~years$

$A=P(1+\frac{r}{n})^{nt}$ $r=9.75$% $=0.0975$ $P=4000$ $A=5000$ $5000=4000(1+\frac{0.0975}{2})^{2t}$ $1.25=(1+\frac{0.0975}{2})^{2t}$ $\log1.25=\log(1+\frac{0.0975}{2})^{2t}$ $\log1.25=2t[\log(1+\frac{0.0975}{2})]$ $t=\frac{\log1.25}{2\log(1+\frac{0.0975}{2})}=2.344$