Question

A sum of money doubles itself at a simple interst in 25/2years.in how many years would it treble itself?

Answer 1

Under compound interest system, the accumulation (principal + interest) at time 't' years of a principal 'a' at a rate of interest 'i' compounded annually is given by:

a(1+i)ta(1+i)t

So, we get the equation:

8a=a(1+i)88a=a(1+i)8

or, 1+i=1+i= 8^(1/8)

Now that we know the interest rate, we have to find the time 't' to it would take for the amount to grow four times. Therefore,

4a=a(1+i)t4a=a(1+i)t

or, 4=[4=[8^(1/8)]t)]t

Taking logs on both sides, we get:

log(4)=t(1/8)log(8)log(4)=t(1/8)log(8)

or, t=8log(4)/log(8)t=8log(4)/log(8)

or, t=5.33t=5.33

So, it would take five years and four months for the amount to grow four times.