Discussion
A certain sum amounts to ₹15,435 in one year at 10% p.a., interest compounded half yearly. What will be the compound interest on the same sum in 3 years at the same rate of interest, compounded yearly?
Answer: D
The compound interest is 4,634. In one year at 10 % compounded half-yearly, the rate is 5 % per half-year for two half-years, so the amount is the principal times 1.1025.
\[ P = \frac{15435}{1.1025} = 14000 \]
Compounded yearly for 3 years at 10 %:
\[ CI = 14000 \times (1.1^3 - 1) \]
\[ = 14000 \times 0.331 = 4634 \]
The options 4,524, 4,554 and 4,624 do not equal 14000 times 0.331, so the fourth option is correct. As a check, 14000 x 1.1025 = 15435, the amount given in the question, and the amount after 3 years at yearly compounding is 14000 x 1.331 = 18634.
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