Finance Question, please help :)?

Question

if a firm's earning per share grew from $1 to $2 over a 10 year period the total growth would be 100 percent, but the anual growth rate would be less than 10 percent. Is this true or false? can you please explain

Answer 1

here, 2 = 1 x e^r x 10
Taking natural log on both sides,
r = Natural log(2/1)/10=6.93 or 7%, So your answer of less than 10% is correct.
This can also be done as discrete compounding as follows,
2=1x(1+r)^10
Taking natural log on both sides
ln(2)/10=ln (1+r)
0.069 = ln(1+r)
there for, (1+r)= e^0.069 and
r= e^0.069 -1 = 0.0714 or 7.14%, which is also less than 10%. So both ways your answer is right it is less than 10%

Answer 2

true

the annual growth rate of any amount doubling in 10 years is about 7.2%.

Thats also the internal rate of return. Its the interest rate that compounded over the period generates the investment result.

Put another way, if you invested the dollar in a savings account paying 7.2% per year, then in ten years the account would grow to: 1.072 x 1.072 x . . . . and after ten years it would be worth $2.

A dollar invested with an annual growth of 10pct per year would be worth $2.59 after ten years.