On January $1$ of last year, an investor bought one share of a public utility stock for $$45,$ which paid a dividend of $3\%$ per annum on a quarterly basis. If there was no change in the stock$$s market value over the course of the year, what was her return on this investment at year$$s end? Now assume that the stock$$s market value increased $10\%$ during the year, on a continuously compounded basis, and each quarter$$s paid dividend was based on the stock$$s value on the last day of the quar$-$ ter. What was the return on this investment at the end of each quarter in dollar terms? What was the investor$$s total annual percentage return based on the origi$-$ nal investment?