Please read the following question and answer i wrote and what would be your response?

5-3 If a firms earnings per share grew from $1 to $2 over a 10-year period, the total growth would be 100%, but the annual growth rate would be less than 10%. True or false? Explain. (Hint: If you arent sure, plug in some numbers and check it out.)

This is true because of compounding as a an annual growth rate of 10% would result in a higher stock price at the end of 10 years. Think of it this way, if the stock started at $1 and went up to 10% to $1.10 at the start of year 2. If the stock price were to go up another 10% by the start of year 3 the stock price would be $1.21 because the initial value of the stock at the beginning of year 2 is greater than it was at the beginning of year 1 meaning a 10% increase adds $.11 to the stock price instead of $.10 from year 1 to 2. Another way to show that this is true is to use the Compounded Annual Growth Formula CARG= (Ending Value/Beginning Value)^1/time -1 CARG=($2/$1)1/10 years - 1= (2)^1/10 -1= 1.0718-1= .0718 therefore the compounded annual growth rate in this problem would actually be 7.18%

5-4. Would you rather have a savings account that pays 5% interest compounded semiannually or one that pays 5% interest compounded daily? Explain.

Compound interest occurs when interest is earned on prior periods' interest. (Brigham & Houston, 2015 page 143) With that concept, the savings account that pays 5% interest compounded daily is certainly a better choice as it will pay more interest with the same rate and period of time. Below is just an simple test to prove my reasoning. Semiannually compounded: $100 saved in the account after 1 year = $105.06 (compounded twice) Daily compounded: $100 saved in the account after 1 year = $105.13 (compounded 365 times)