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how long would it take for 1000 deposited in an account payinv 6% interest
compounded countinously to earn 200 interest
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Formula for the future value of a continuously compounded account in this problem is
FV = ,
where "t" is in years, "e" is the base of natural logarithms.
So, we write for the total
1000 + 200 =
or
1200 = .
Now we solve this equation, step by step, and find time "t".
=
1.2 = =
Next, take the natural logarithm of both sides
ln(1.2) = 0.06*t
t = = 3.038692613
So, the ANSWER is that the time to earn 200 interest is about 3 years.
(More precisely, 3 years and 15 days).
Solved.
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To see many other similar (and different) solved problems on continuously compounded accounts, look into the lesson
- Problems on continuously compound accounts
in this site.
After reading this lesson, you will tackle such problems on your own without asking for help from outside.