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If Rs. 125000 amounts to Rs. 140608 at 8% compound interest, interest being compounded semi-annually in certain time period. If the same amount is invested at same rate of interest and time, the amount of simple interest is?1). Rs. 1400002). Rs. 1450003). Rs. 1500004). Rs. 200000 |
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Answer» Given Sum(Principal) = Rs. 125000 Amount at the end compounded semiannually = Rs. 140608 RATE of interest per annum (r) = 8% For semiannual compounding, the interest rate will be HALVED = (8/2)% = 4% From the equation of COMPOUND interest, Amount = Principal [1 + (r/100)]2n ⇒ 140608 = 125000(1 + (4/100))2n ⇒ 140608/125000 = (104/100)2n ⇒ (52/50)3 = (52/50)2n As bases are equal, equalize the powers, n = 3/2 = 1.5 Formula for Amount under Simple Interest (A) = P [1 + (nr/100)] ⇒ A = 125000 [1 + (12/100)] ⇒ A = 125000 (1 + 0.12) ⇒ A = 125000 × 1.12 ⇒ A = Rs. 140000 ∴ Amount = Rs. 140000 |
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