The compound interest on a certain sum for 1 year at 8% p.a., interest compounded half-yearly, is ₹652.80. What will be the simple interest on the same sum for 2121\over221years at the same rate of interest? A₹1,680 B₹1,720 C₹1,740 D₹1,600 Show answer & explanationCorrect answer: DExplanationThe correct answer is option 4 i.e. ₹1,600. R = 82=4%\frac{8}{2} = 4\%28=4% per half-year n = 2 CI=P(1+r100)n−P=P[(1+4100)2−1]CI = P \left(1 + \frac{r}{100}\right)^n - P = P \left[ \left(1 + \frac{4}{100} \right)^2 - 1 \right]CI=P(1+100r)n−P=P[(1+1004)2−1] CI=P[(1.04)2−1]=P(1.0816−1)=P⋅0.0816CI = P \left[ (1.04)^2 - 1 \right] = P(1.0816 - 1) = P \cdot 0.0816CI=P[(1.04)2−1]=P(1.0816−1)=P⋅0.0816 CI=652.80=P⋅0.0816⇒P=652.800.0816=₹8000CI = 652.80 = P \cdot 0.0816 \Rightarrow P = \frac{652.80}{0.0816} = ₹8000CI=652.80=P⋅0.0816⇒P=0.0816652.80=₹8000 SI=P⋅R⋅T100=8000⋅8⋅2.5100SI = \frac{P \cdot R \cdot T}{100} = \frac{8000 \cdot 8 \cdot 2.5}{100}SI=100P⋅R⋅T=1008000⋅8⋅2.5 SI=160000100=₹1600SI = \frac{160000}{100} = ₹1600SI=100160000=₹1600