Question

the value of a stock is expected to increase by 8% per year. based on that rate, which of the following statements is accurate about the value of the stock after ten years?
a the value of the stock will increase by 80%
b the value of the stock will increase by less than 80%
c the value of the stock will increase by more than 80%
d we dont have enough information to predict the relative value after 10 years

Explanation:

Step1: Define compound growth formula

Let initial value be $P$, final value $A$, rate $r=0.08$, time $t=10$. The formula is:
$$A = P(1+r)^t$$

Step2: Calculate growth factor

Substitute values to find total multiple:
$$(1+0.08)^{10} = 1.08^{10} \approx 2.1589$$

Step3: Compute percentage increase

Subtract 1 and convert to percentage:
$$(2.1589 - 1) \times 100\% = 115.89\%$$

Step4: Compare to 80%

$115.89\% > 80\%$, so growth exceeds 80%.

Answer:

C. The value of the stock will increase by more than 80%