Question

calculate the rate of interest in percentage of per annum of compound interest if Rs 5000 becomes 20000 in 4 years.

Answer 1

The rate of interest in the percentage of per annum of compound interest is 41.4%.

Step-by-step explanation:

Required formula:

A = P [1 + $\frac{R}{100}$]ⁿ

Principal, P = Rs. 5000

Amount, A = Rs. 20000

Time period, T = 4 years

Now, substituting the given values in the formula we can solve the above question by two methods:

Method 1: By using the antilog  

20000 = 5000 [1 + R/100]⁴

⇒ [20000/5000] = [1 + R/100]⁴

⇒ [1 + R/100]⁴ = 4

Taking log on both sides

⇒ 4 log [1 + R/100] = log 4 …… [∵ log aᵇ = b log a]

⇒ 4 log [1 + R/100] = 0.602

⇒ log [1 + R/100] = 0.1505

Taking antilog on both sides (please refer to the antilog table from the internet for the value of antilog 0.1505)

⇒ [1 + R/100] = 1.414  

⇒ R/100 = 0.414

⇒ R = 41.4%

Method 2: Using (¼) power on both sides

20000 = 5000 [1 + R/100]⁴

⇒ [20000/5000] = [1 + R/100]⁴

⇒ [1 + R/100]⁴ = 4

Taking power of (1/4) on both sides

⇒ [1 + R/100] = [4]^(1/4)  

⇒ [1 + R/100] = 1.414  

⇒ R/100 = 0.414

⇒ R = 41.4%

Thus, the rate of interest is 41.4% per annum of compound interest.

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