The value of a stock increases at a rate of 1/2% per year. If the initial value of the stock $40 a share, when will the value of the stock be $50? Round your answer to the nearest tenth of a year

After 45.7 years

Step-by-step explanation:

∵ r = 1/2% per year

∵ P0 = $40

∵ Pn = $50

∵ Pn = P0 (1 + r/100) ^n-1

∵ P0 is initial value, Pn is the value after n years, is the rate

∴ 50 = 40 (1 + 0.5/100) ^n-1

∴ 50/40 = (1.005) ^n-1

∴ 1.25 = (1.005) ^n-1 ⇒ insert ln in both sides

∴ ln (1.25) = (n-1) ln (1.005)

∴ n - 1 = ln (1.25) / ln (1.005)

∴ n = ln (1.25) / ln (1.005) + 1 = 45.7 years