- If a sum of money grows to 144/121 times when invested for two years in
a scheme where interest is compounded annually, how long will the same sum
of money take to treble if invested at the same rate of interest in a scheme
where interest is computed using simple interest method?
(1) 9 years (2) 22 years (3) 18 years (4) 33 years
Solution:
The sum of money grows to
times in 2 years.
If P is the principal invested, then it has grown to
P
in two years when invested in compound interest.
In compound interest, if a sum is invested for two years, the amount is found
using the following formula
A=P(1+(r/100))^2 =
P
in this case.
=>(1+ (r/100) )^2=144/121 => (1+ (r/100))^2=(12/11)^2 => 1+ (r/100)=12/11
=> r/100 = 1/11 => r=100/11
If r = (100/11) %, then in simple interest the time it will take for a sum of
money to treble is found out as follows:
Let P be the principal invested. Therefore, if the principal trebles = 3P, the
remaining 2P has come on account of simple interest.
Simple Interest = Pnr/100, where P is the simple interest, r is the rate
of interest and �n� is the number of years the principal was invested.
Therefore, 2P = (Pn*100) / (11*100) => 2 =
or n = 22 years.
