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Suppose that if you purchase one share of the initial offering of Sentient Machines Incorporated stock in the year 2010 for $30, it will be worth about $1,000,000 in 2040. What's the annual interest rate of this investment, assuming continuous compounding? Round your answer to the nearest hundredth of a percent.

Respuesta :

Answer:

annual interest rate is 34.71%

Explanation:

given data

principal P = $30

amount  A = $1000000

time period t = 30 year

to find out

annual interest rate (r)

solution

we know here  continuous compounding

so continuous compounding formula is

amount = principal × [tex]e^{rt}[/tex]     ...........1

put here all value in equation 1

amount = principal × [tex]e^{rt}[/tex]

1000000 = 30 × [tex]e^{30r}[/tex]

take ln both side

ln 33333.333 = ln [tex]e^{30r}[/tex]

10.4143 = 30 r

so r = 10.4143 / 30

rate = 0.3471 = 34.71%

so annual interest rate is 34.71%

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