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# Interest?

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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
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#1
+92254
+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

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check

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

Melody  Dec 22, 2017
#2
+804
+2

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

Julius  Dec 22, 2017
#3
+804
+3

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

Also how did the A go away?

Julius  Dec 22, 2017
#4
+92254
+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.

Melody  Dec 22, 2017
#5
+804
+2

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

Julius  Dec 22, 2017
#6
+92254
+2

You are very welcome :)

Melody  Dec 22, 2017

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