Asked by Amber
An initial investment in an account in which interest is compounded repeatedly is $813. If the time doubles the amount in 9 1/4 years, what's the annual rate going to end up being?
Answers
Answered by
Reiny
I don't like the wording "repeatedly"
Usually this type of question uses "continuously" to describe the increase.
amount = a e^(kt) , where k is the annual rate , t is the time in years and a is the initial amount.
e^(k(9.25)) = 2
take ln of both sides
9.25k ln e = ln 2 , but lne = 1
9.25k = ln2
k = .0749..
or appr. 7.5%
Usually this type of question uses "continuously" to describe the increase.
amount = a e^(kt) , where k is the annual rate , t is the time in years and a is the initial amount.
e^(k(9.25)) = 2
take ln of both sides
9.25k ln e = ln 2 , but lne = 1
9.25k = ln2
k = .0749..
or appr. 7.5%
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