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If you invested money into an account that pays 9%/a compounded weekly, how many years would it take for your deposit to double?

Julius  Dec 22, 2017
 #1
avatar+92805 
+4

If you invested money into an account that pays 9%/a compounded weekly, how many years would it take for your deposit to double?

 

\(2A=A(1+\frac{0.09}{52})^{n}\\ 2=(1+\frac{0.09}{52})^{n}\\ log2=log(1+\frac{0.09}{52})^{n}\\ log2=nlog(1+\frac{0.09}{52})\\ n=log2\div log(1+\frac{0.09}{52})\\\)

 

log(2)/log(1+0.09/52 = 400.831511360387616 weeks

400.831511360387616/52 = 7.708298295392069538

 

7.7 years

 

---------------------------------------------------------------

check

1*(1+0.09/52)^400.83 = 1.9999947728968765

Melody  Dec 22, 2017
 #2
avatar+946 
+2

Why did you do 0.09/52? I understand 0.09 but why 52? 

Julius  Dec 22, 2017
 #3
avatar+946 
+3

Oh never mind, there is 52 weeks in a year :D 

 

Also how did the A go away? 

Julius  Dec 22, 2017
 #4
avatar+92805 
+2

The A stands for any Amount. 

There is 1 of them at the start and there must be 2 of them at the end. 

I just divided both sides by A to get rid of the A.

 

I could just have easily have said there was $1 at the beginning and $2 at the end and then I would not have needed the A at all.   laugh

Melody  Dec 22, 2017
 #5
avatar+946 
+2

I see :) Thank you for your help and time. 

Julius  Dec 22, 2017
 #6
avatar+92805 
+2

You are very welcome :)

Melody  Dec 22, 2017

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