Krish C. answered • 6d

Highly-Rated Mathematics Tutor

Consider the initial investment as x

We want the final amount to be 3x

Applying the compound interest formula

Amount = (Initial Amount)*(1+Rate)*(1+Rate)*(1+Rate) (multiply rate as many years to be interested)

So let the time be n years

We have, 3x = x*(1+0.04)^{n}

i.e. 3 = 1.04^{n}

Taking log to the base 1.04 on both sides, log_{1.04}3 = log_{1.04}1.04^{n}

By the rules of logarithm, log_{1.04}3 = n*log_{1.04}1.04 = n*1 = n

Now you can either put it directly into your calculator and get

n = log_{1.04}3 = 28.011 years

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