Answer
about 2 years and 4 months
Work Step by Step
If a principal $P$ is invested in an account paying an annual interest rate $r$, compounded $n$ times a year, then after $t$ years the amount $A(t)$ in the account is
$A(t)=P(1+\displaystyle \frac{r}{n})^{nt}$
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Solve for t after inserting given values
$5000 =4000(1+\displaystyle \frac{0.0975}{2})^{2t} \qquad$ ... $/\div 4000$
$1.25 =(1.04875)^{2t} \qquad$ ... apply log() to both sides
$\log 1.25=2t\log 1.04875 \qquad$ ... $/\div(2\log 1.04875)$
$t=\displaystyle \frac{\log 1.25}{2\log 1.04875}\approx 2.344.$
($0.344$ years $\approx $4 months)
So, to save $\$ 5000$, it takes about 2 years and 4 months
