Find the interest on Rs. 19,000 for 2 years at the rate of 40% per yea

1.	Find the interest on Rs. 19,000 for 2 years at the rate of 40% per year compounded semi annually.1. Rs. 20,548.42. Rs. 20,398.43. Rs. 15,548.54. Rs. 30,548.4
Answer» Correct Answer - Option 2 : Rs. 20,398.4 Given: Principle = 19000 Time = 2 years Rate = 40% Condition = Semi annually Concept used: The interest compounded is Semi-annually ( half yearly ) New rate = Rate/2 New time = Time × 2 Formula used: C.P = P{(1 + R/100)^T – 1} Where, C.P → Compound interest P → Principal R → Rate T → Time Calculations: New rate = 40/2 = 20% New time = 2 × 2 = 4 C.P = P{(1 + R/100)T – 1} ⇒ 19000{(1 + 20/100)⁴ – 1} ⇒ 19000{(1 + 1/5)⁴ – 1} ⇒ 19000 {(6/5)⁴ – 1} ⇒ 19000 {(6/5 × 6/5 × 6/5 × 6/5) – 1} ⇒ 19000{(1296/625) – 1} ⇒ 19000(1296 – 625)/625 ⇒ 19000 × (671/625) ⇒ 30.4 × 671 ⇒ Rs. 20,398.4 ∴ The compound interest is Rs. 20,398.4

Find the interest on Rs. 19,000 for 2 years at the rate of 40% per year compounded semi annually.1. Rs. 20,548.42. Rs. 20,398.43. Rs. 15,548.54. Rs. 30,548.4

Answer» Correct Answer - Option 2 : Rs. 20,398.4

Given:

Principle = 19000

Time = 2 years

Rate = 40%

Condition = Semi annually

Concept used:

The interest compounded is Semi-annually ( half yearly )

New rate = Rate/2

New time = Time × 2

Formula used:

C.P = P{(1 + R/100)^T – 1}

Where,

C.P → Compound interest

P → Principal

R → Rate

T → Time

Calculations:

New rate = 40/2 = 20%

New time = 2 × 2 = 4

C.P = P{(1 + R/100)T – 1}

⇒ 19000{(1 + 20/100)⁴ – 1}

⇒ 19000{(1 + 1/5)⁴ – 1}

⇒ 19000 {(6/5)⁴ – 1}

⇒ 19000 {(6/5 × 6/5 × 6/5 × 6/5) – 1}

⇒ 19000{(1296/625) – 1}

⇒ 19000(1296 – 625)/625

⇒ 19000 × (671/625)

⇒ 30.4 × 671

⇒ Rs. 20,398.4

∴ The compound interest is Rs. 20,398.4

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