The value of a particular investment follows a pattern of exponential growth. You invested money in a money market account. The value of your investment t years after your initial investment is given by the exponential growth model A=2600e^0.08t . By what percentage is the account increasing each year?
2 answers
recall that a rate of r compounded continuously is e^rt
You are finding the equivalent annual rate equal to 8% per annum compounded continuously, that is
(1 + i)^t = e^.08t
take the tth root of both sides
1+i = e^.08 = 1.083287...
i = 0.832...
check, suppose we take 5 years
amount using your formula = 2600 e^5*.08) = 3878.74
amount using interest formul = 2600(1.083287..)^5 = 3878.74
well, well, ...
(1 + i)^t = e^.08t
take the tth root of both sides
1+i = e^.08 = 1.083287...
i = 0.832...
check, suppose we take 5 years
amount using your formula = 2600 e^5*.08) = 3878.74
amount using interest formul = 2600(1.083287..)^5 = 3878.74
well, well, ...