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The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. Find the amount to be paid to clear a debt of Rs. 50000 in 3 years, when the interest is compounded annually and the interest rate increases by 50% each year. I) Interest rate for first year is 2%. II) Interest rate for second year is 3%. III) Interest rate for third year is 4.5%.

The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. Find the amount to be paid to clear a debt of Rs. 50000 in 3 years, when the interest is compounded annually and the interest rate increases by 50% each year. I) Interest rate for first year is 2%. II) Interest rate for second year is 3%. III) Interest rate for third year is 4.5%. Correct Answer Any one

When the interest is compounded annually at difference interest rates,

Amount = Principal × (1 + R1/100) × (1 + R2/100) × (1 + R3/100)

Considering statement I,

R1 = 2%

R2 = (100 + 50)% of R1 = 1.5 × 2 = 3%

R3 = (100 + 50)% of R2 = 1.5 × 3 = 4.5%

Amount = 50000 × (1 + 2/100) × (1 + 3/100) × (1 + 4.5/100) = Rs. 54893.85

Considering statement II,

R2 = 3%

R2 = (100 + 50)% of R1

⇒ R1 = 3/1.5 = 2%

R3 = (100 + 50)% of R2 = 1.5 × 3 = 4.5%

Amount = 50000 × (1 + 2/100) × (1 + 3/100) × (1 + 4.5/100) = Rs. 54893.85

Considering statement III,

R3 = 4.5%

R3 = (100 + 50)% of R2

⇒ R2 = 4.5/1.5 = 3%

R2 = (100 + 50)% of R1

⇒ R1 = 3/1.5 = 2%

Amount = 50000 × (1 + 2/100) × (1 + 3/100) × (1 + 4.5/100) = Rs. 54893.85

∴ The question can be answered using any one of the given statements

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