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**+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

#4**+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