How long will it take to for an investment to triple if interest is compounded continuously At 4%?

Answer 1

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 = 1.04ⁿ

Taking log to the base 1.04 on both sides, log_1.043 = log_1.041.04ⁿ

By the rules of logarithm, log_1.043 = n*log_1.041.04 = n*1 = n

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

n = log_1.043 = 28.011 years

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