SOLUTION: How long will it take to earn your first million dollars if you annually invest $1000 into an IRA at 10% interest compounded monthly. This answer should be calculated using logar

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Question 967716: How long will it take to earn your first million dollars if you annually invest $1000 into an IRA at 10% interest compounded monthly.
This answer should be calculated using logarithms so that the answer is exact.

Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

To calculate this value exactly, a fairly simple formula can be utilized.

=principal ()
=annual nominal interest rate ()
=number of compounding during year (, because of months)
=number of years (unknown)
=amount after years (first )
This formula yields results when we have the time known, but in this case we need to isolate "" for the time necessary for the principal to turn into $. So we need to rearrange the formula into a fairly complex logarithmic formula:






Then substitute the numbers into the equation -



Finally we got the answer - it'll take about years and a four months!!!

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
How long will it take to earn your first million dollars if you annually invest $1000 into an IRA at 10% interest compounded monthly.
This answer should be calculated using logarithms so that the answer is exact.
Use Future Value of Ordinary Annuity formula: 





------ Cross-multiplying



---------- Exponential form
-------- Logarithmic form
---------- Applying change of base

years ------ EXACT TIME
years ------------ APPROXIMATE TIME
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