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?
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)