Stock $Y$ is currently priced at $25$ per share and it pays dividends

continuously at a rate propertional to its price at a constant rate of $3,5\%.$

You purclase $100$ shares of stock $Y$ and invest all dividends by purclasing

extra shares of stock Y$.$ After $4$ months, you close out all positions

when the stock price is $S_{\frac{1}{3}}.$

If the $4-$month profit is $0$ when the continuously compourded

risk$-$free interest rate is $2\mathrm{.}5\%,$ find $S_{\frac{1}{3}}.$

Hint: prefit $=$ value at time $\frac{1}{3}-$ FV of cost at time $0.$

$0=S_{\frac{1}{3}}$ubrace$(100e^{0\mathrm{.}035\frac{1}{3}}$ubrace${)}_{\frac{?}{?}\text{\#}\text{s}\text{h}\text{a}\text{r}\text{e}\text{s}}-25100e^{0\mathrm{.}025\frac{1}{3}}$