# if a sum of money grows to 144/121 times when invested for 2 years in a scheme where the interest is compounded annually ,then how long will the same sum take to triple if invested at the same rate...

if a sum of money grows to 144/121 times when invested for 2 years in a scheme where the interest is compounded annually ,

then how long will the same sum take to triple if invested at the same rate of interest in a simple interest scheme?

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### 2 Answers

Let us assume that the yearly rate of interest is R. Now we are given that in 2 years the amount invested becomes 144/121 times.

We also know that when interest is compounded annually, an amount A in n terms becomes A*(1+R)^r, where R is the rate of interest.

So A*(1+R)^2 = (144/121)*A

=>(1+R)^2 = 144/121

=> 1+ R = 12 /11

=> R = 1/ 11

Now we need to find how many years a sum of money invested at the same rate of interest but simple interest instead of compound takes to become triple.

3*A = A*(1+RN)

=> 3 = 1 + (1/11)N

=> 2 = (1/11)N

=> N = 2*11

=> N = 22

**Therefore the money invested at simple interest will triple in 22 years.**

The principle P becomes 144/121 times in 2 years in a compound interest annual.

Therefore P(144/121) = P(1+r)^2

144/121 = (1+r)^2.

We take square root.

12/11 = 1+r

12/11 -1 = r

r = (12-11/)11 = 1/11.

Therefore (100/11)% is the rate of annual interest.

So for n years the simple interest = Pnr/100 = Pn (100/11)/100 = Pn/11.

So along wirh principle and the interest ,the amount P+Pn/11

If it takes n years to triple the ampount , 3P = P+Pn/11

3 = 1+n/11

n/11 = 3-1=2

n = 2*11 = 22.

Therefore it takes 22 years for the Principle along with a simple interest of (100/11)% PA to become 3 times itself(principle)