What does the interest rate have to be, if a bank pays interest, compounded continuously and the amount doubles in 5 years?

Question

Mathematics

Kale Flores

10 June, 20:48

What does the interest rate have to be, if a bank pays interest, compounded continuously and the amount doubles in 5 years?

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Lyric Dyer · Answer 1

Let the original amount be A. Double that would be 2A.

Then, 2A = Ae^ (r*5), or 2 = e^ (5r).

Taking the natural log of both sides: ln 2 = 5r. Then r = (ln 2) / 5 = 0.14

The interest rate would have to be 13.86% per year, written here as r=0.14.