Question

if a certain amount on compound interest doubles itself in 5 years, in how many years will it become 8 times itself with same rate of interest ?

Answer 1

Let,

Principal = Rs. 100.

Amount = Rs. 200.

Rate = r%

Time = 4 years.

Now,

A = P*[1+ (r/100)]n;

200 = 100*[1+(r/100)]4;

2 = [1+(r/100)]4; ........... (i)

If sum become 8 times in the time n years,

then,

8 = (1+(r/100))n;

23 = (1+(r/100))n; ........ (ii)

Using eqn (i) in (ii), we get;

([1+(r/100)]4)3 = (1+(r/100))n;

[1+(r/100)]12 = (1+(r/100))n;

Thus, n = 12 years.