The principal of Rs. 75,000 turns Rs. 1,03,950 in 3 years. If the rate

1.	The principal of Rs. 75,000 turns Rs. 1,03,950 in 3 years. If the rate of interest for the first year is 5% per annum and for the second-year rate of interest is 10% per annum, then find the rate of interest for the third year compounded yearly?1. 20%2. 15%3. 25%4. 10%
Answer» Correct Answer - Option 1 : 20% Given: Rate of interest for first year = 5% Rate of interest for second year = 10% Time = 3 years Amount = Rs. 1,03,950 Principal = Rs. 75,000 Concept used: A = P(1 + R₁/100)(1 + R₂/100)(1 + R₃/100) Where, A → Amount P → Principal R → Rate Calculations: A = P(1 + R1/100)(1 + R2/100)(1 + R3/100) ⇒ 103950 = 75000(1 + 5/100)(1 + 10/100)(1 + R₃/100) ⇒ 103950 = 75000 × (21/20)(11/10)(1 + R₃/100) ⇒ 103950 = 86625 × (1 + R₃/100) ⇒ 103950/86625 = (1 + R₃/100) ⇒ 1.2 × 100 = 100 + R₃ ⇒ 120 = 100 + R₃ ⇒ R₃= 20% ∴ Rate of interest for the third year is 20%

The principal of Rs. 75,000 turns Rs. 1,03,950 in 3 years. If the rate of interest for the first year is 5% per annum and for the second-year rate of interest is 10% per annum, then find the rate of interest for the third year compounded yearly?1. 20%2. 15%3. 25%4. 10%

Answer» Correct Answer - Option 1 : 20%

Given:

Rate of interest for first year = 5%

Rate of interest for second year = 10%

Time = 3 years

Amount = Rs. 1,03,950

Principal = Rs. 75,000

Concept used:

A = P(1 + R₁/100)(1 + R₂/100)(1 + R₃/100)

Where,

A → Amount

P → Principal

R → Rate

Calculations:

A = P(1 + R1/100)(1 + R2/100)(1 + R3/100)

⇒ 103950 = 75000(1 + 5/100)(1 + 10/100)(1 + R₃/100)

⇒ 103950 = 75000 × (21/20)(11/10)(1 + R₃/100)

⇒ 103950 = 86625 × (1 + R₃/100)

⇒ 103950/86625 = (1 + R₃/100)

⇒ 1.2 × 100 = 100 + R₃

⇒ 120 = 100 + R₃

⇒ R₃= 20%

∴ Rate of interest for the third year is 20%

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