The compound interest (in Rs.) on a sum of Rs. 12,000 at 10% per annum

1.	The compound interest (in Rs.) on a sum of Rs. 12,000 at 10% per annum for 1.5 years, interest compounded half-yearly, is:1. Rs. 1,7502. Rs. 1,9003. Rs. 1,821.504. Rs. 1,891.50
Answer» Correct Answer - Option 4 : Rs. 1,891.50 Given: A sum = Rs. 12,000 Rate = 10% per annum And time = 1.5 years. Formula used: Amount = Principal{1 + (R/100)}ⁿ Where n = time in years and R = rate percentage/annum Compund interest = Amount - Principal If time = n years, rate = R% and interest compounded half-yearly Then time = 2n and rate = (R/2)% Calculation: Interest compounded half-yearly: Then time = 2 × 1.5 ⇒ 3 years And the rate = 10/2 ⇒ 5% Amount = 12000 × {1 + (5/100)}³ ⇒ 12000 × {1 + (1/20)}³ ⇒ 12000 × {(20 + 1)/20}³ ⇒ 12000 × (21/20)³ ⇒ 12000 × (9261/8000) ⇒ 12 × 9261/8 ⇒ 1,11,132/8 ⇒ Rs. 13891.5 Compound interest = amount - principal ⇒ 13891.5 - 12000 ⇒ Rs. 1891.5 ∴ The compound interest is Rs. 1891.5

The compound interest (in Rs.) on a sum of Rs. 12,000 at 10% per annum for 1.5 years, interest compounded half-yearly, is:1. Rs. 1,7502. Rs. 1,9003. Rs. 1,821.504. Rs. 1,891.50

Answer» Correct Answer - Option 4 : Rs. 1,891.50

Given:

A sum = Rs. 12,000

Rate = 10% per annum

And time = 1.5 years.

Formula used:

Amount = Principal{1 + (R/100)}ⁿ

Where n = time in years and R = rate percentage/annum

Compund interest = Amount - Principal

If time = n years, rate = R% and interest compounded half-yearly

Then time = 2n and rate = (R/2)%

Calculation:

Interest compounded half-yearly:

Then time = 2 × 1.5

⇒ 3 years

And the rate = 10/2

⇒ 5%

Amount = 12000 × {1 + (5/100)}³

⇒ 12000 × {1 + (1/20)}³

⇒ 12000 × {(20 + 1)/20}³

⇒ 12000 × (21/20)³

⇒ 12000 × (9261/8000)

⇒ 12 × 9261/8

⇒ 1,11,132/8

⇒ Rs. 13891.5

Compound interest = amount - principal

⇒ 13891.5 - 12000

⇒ Rs. 1891.5

∴ The compound interest is Rs. 1891.5

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