# If it will take your money 18 years to double, what is the rate of interest that you are earning?

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Let P be the principle.

case (i):

Simple interest:

let r be the rate of interest.

Then by simple interest in 18 years, we get an interst of principle *number of years * rate of interst= P*18*r/100.

So the amount we get atfter 18 years = Principle + interest = P+18pr/100 which is doule P.

Therefore P+18Pr/100 = 2P.

Divide by P and multiply by 100 :

(100/P)(P+18Pr/100) = (100/P)2P

100 +18r = 200.

18r = 200-100 = 100.

Therefore 18r = 100.

So r = 100/18 = 50/9 .

Or r = (50/9)% simple interest.

Case (ii):

Compound interest:

We assume that r % is the annual interest compounded every year.

So the amount we get for a principle of P after n years is given by:

P(1+r/100)^n .

So after 18 years the amount is P(1+r/100)^18 which should be twice P.

Therefore P(1+r/100)^18 = 2P.

(1+r/100)^18 = 2.

1+r/100 = 2^(1/18).

r = 100{2^(1/18)-1}%.

r = 3.9259% approximately.