Question

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.

Answer 1

annual interest rate is 34.71%

Step-by-step 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 ×
`e^(rt)` ...........1

put here all value in equation 1

amount = principal ×
`e^(rt)`

1000000 = 30 ×
`e^(30r)`

take ln both side

ln 33333.333 = ln
`e^(30r)`

10.4143 = 30 r

so r = 10.4143 / 30

rate = 0.3471 = 34.71%

so annual interest rate is 34.71%