Question

on a certain principal if the simple interest for 2 years is Rs 6000 and compound interest for the 2 years is Rs 6900. find the principal?​

Answer 1

Answer:

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Answer 2

Answer:

Let the principal be denoted as Rs. “P” and the rate of interest be denoted as “R”%.

Step 1:

Simple interest, S.I. = Rs. 6000

Time, T = 2 years

∴ S.I. = [PRT]/100

⇒ 6000 = [PR*2]/100

⇒ PR = 6000*100/2

⇒ PR = 300000 …… (i)

Step 2:

Compound Interest, C.I. = Rs. 6900

Time, n = 2 years

∴ C.I. = P [(1+R/100)ⁿ - 1]

⇒ 6900 = P [(1+R/100)² - 1]

⇒ 6900 = P [1 + (2R/100) + (R²/100²) - 1]

⇒ 6900 = PR/100 [2 + R/100]

Substituting value of PR from eq. (i)

⇒ 6900 = 300000/100 [2 + R/100]

⇒ 2 + R/100 = 6900 / 3000

⇒ R/100 = 2.3 – 2  

⇒ R = 30%

Step 3:

Substituting the value of R in eq. (i)

PR = 300000

⇒ P * 30 = 300000

⇒ P = 300000/30

⇒ P = Rs. 10,000

Thus the principal is Rs. 10,000.