Question

A certain sum is invested for certain time .It amount to rs.400 at 10% per annum.But when invested at 4% per annum it amount to rs.200. Find the time

Answer 1

Answer:

Step-by-step explanation:

In this case we will use the compound interest accumulation factor.

The compound interest accumulation factor is given as :

P(1 + i)^n = A

Where :

P = Principle amount.

n = Time

A = Accumulated amount.

We substitute for both of them.

P(1. 1)^n = 400

P = 400/(1.1)^n

P(1.04)^n = 200

P = 200/(1.04)^n

Since in both cases P is equal we equate the two to get the unknowns.

We have :

200/(1.04)^n = 400/(1.1)^n

400(1.04)^n = 200(1.1)^n

400/200 = (1.1)^n/(1.04)^n

2^1/n = 1.05769

2 = (1.05769)^n

log 2 = n log (1.05769)

0.30103 = 0.024358n

n = 0.30103/0.024358

n = 12.36

The time is approximately 12 years.