Question

the CI on 10,000 is 1025 at the rate of 5% compounded half yearly for a period of time. find the time​

Answer 1

this is the correct answer

Answer 2

Therefore the time taken to get the compound interest of Rs. 1025 is 2 years.

Given:

The principal amount = P = Rs. 10,000/-

Compound Interest = CI = Rs. 1025/-

Rate of interest = i = 5%

The number of equal periods if compounded half yearly = n = 2

Number of years = T

To Find:

The number of years taken to get the given compound interest.

Solution:

The given question can be solved as shown below.

⇒ Compound Interest = CI = P ( 1 + R/100n $)^n^T$ - P

⇒ 1,025 = 10,000 ( 1 + 5/(100 × 2 ) $)^2^T$ - 10,000

⇒ 1,025 = 10,000 [ (1 + 0.025 $)^2^T$ - 1 ]

⇒ 0.1025 = (1.025 $)^2^T$ - 1

⇒ 1.1025 = (1.025 $)^2^T$

Taking ln on both sides,

⇒ ln ( 1.1025 ) = ln (1.025 $)^2^T$

⇒ ln ( 1.1025 ) = 2T ln (1.025)

⇒ 0.0976 = 2T × 0.0247

⇒ T = 0.0976/0.0494 = 1.97 ≅ 2

Therefore the time taken to get the compound interest of Rs. 1025 is 2 years.

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