Diana R.
asked 05/18/14How can you solve this question with these formulas
A=P(1+r/n)nt
N=N0(1/2) t/h
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Leeland C. answered 05/18/14
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Mathematics and English expert through High School level classes
All you need is the first equation.
Amount = Investment(1+rate/number of times it is compounded)^(number of times it is compounded*time)
Since the final amount we are looking for is double the initial investment of 1000, A=2000 and P=1000. Since the rate is 8%, r=0.08. Since it is compounded semi annually (or twice a year), n=2. So you end up with:
2000=1000(1+0.08/2)^2t -> 2=(1+0.08/2)^2t -> 2=(1.04)^2t
Turn the equation into a logarithm.
log1.042=2t -> t=(1/2)(log1.042) -> t=(1/2)(log2/log1.04) -> t=(1/2)(17.7) -> t=8.85
It would take approximately 8.85 years.
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