Question
A certain sum becomes Rs 13650 at 15% p.a. simple
interest after 2 years. What will be the amount (in RS) of the same sum after 1 year at the same rate of interest, if the interest is compounded half yearly? (nearest to a Rs)Solution
Let the Principal be Rs. x S.I = Rs. (13650 – x) According to the question, ⇒ (x × 15 × 2)/100 = 13650 – x ⇒ 3x/10 = 13650 – x ⇒ 3x = 136500 – 10x ⇒ 13x = 136500 ⇒ x = 10500 Now, if rate of interest is compounded half yearly, the interest becomes half and time becomes twice. So, Rate of interest = 15% ÷ 2 = 7.5% Time period = 1 × 2 = 2 years Now, amount after 1 year = Rs. 10500 × (107.5/100) ⇒ Rs. 12134.0625 ≈ Rs. 12134 ∴ Amount becomes Rs. 12134 after 1 year if compounded half yearly.
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