Question

A sum of money rs. 2000 amounts to 4000 in two years at compound interest . in how many years will the same amount become rs. 8000 .​

Answer 1

Principal (P) = ₹2,000

Amount ( A1) = ₹4,000

Time (T1) = 2 years

Rate of compound interest = say, r % per annum.

A1 = P *(1+ r /100)^2

So, 2,000 *( 1 + r / 100 )^2 = 4000

Or, (1 + r / 100)^2 = 4000 / 2000 =2

So, (1 + r /100) = √2 = 1.414

Now, Amount, A2 = ₹8,000

P = ₹2,000

Time = say, T2

(1+ r/ 100) = 1.414 .. as calculated above

So, A2 = 8,000 = 2,000 * (1.414)^T2 where T2 is the number of years in which ₹2,000 will amount to ₹8,000 at the same rate of annual compound interest, r %.

So, (1.414) ^T2 = 8,000 / 2,000 = 4

We know that 4 = 2 * 2 =(1.414) ^2 * (1.414)^2 = (1.414)^4

So, T2 = 4 years.

Therefore, ₹2,000 will amount to ₹8,000 in 4 years at the given rate of interest compounded annually.

Answer 2

Answer:

the answer of the question is 6 years