Finance pls!?

Question

share of preferred stock pays a quarterly dividend of $1.00. If the price of the stock is $50, what is the effective annual (not nominal) rate of return on the preferred stock?

Answer 1

nominal rate, or annual percentage rate (APR) = 8%

effective rate, or effective annual rate (EAR) = 8.24% (rounded to 2 decimal places)

you should only use the EAR if you assume reinvesting of dividends.

Answer 2

If you use the equation Po=(D1)/(R) you get

50 = (1.00) / (R)

Multipy both sides by R to get

50R = 1.00

Divide both sides by 50 to get

R= .02 or 2 % quarterly, which is 8% annually

So if we use the EAR equation of {(1+ (Q/M)) ^M}  - 1, with Q being the quoted rate and M being the number of coumpounding periods we get:

{(1+ (.08/4)) ^4}  - 1

Doing the math (.08/4) = .02 so we have:

{(1.02)^4} - 1

This gives us:

( 1.08243216) - 1

and we are left with:

.08243216 or 8.243216%