You have a 1000 to invest in an account with a rate of 8% compounded semi annually. How long will it take you to double your money? (2024)

Algebra 2 Algebra Help Algebra Word Problem

Diana R.

asked 05/18/14

How can you solve this question with these formulas

A=P(1+r/n)nt

N=N0(1/2) t/h

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1 Expert Answer

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Leeland C. answered 05/18/14

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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.

log_1.042=2t -> t=(1/2)(log_1.042) -> 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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You have a 1000 to invest in an account with a rate of 8% compounded semi annually. How long will it take you to double your money? (2024)

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