The difference between compound interest and simple interest on a sum for 2 years at 10\% per annum, when the interest is compounded annually is ₹ 16. If the interest were compounded half-yearly, the difference in two interests would be
(a)₹ 24.81
(b)₹ 26.90
(c)₹ 31.61
(d)₹ 32.40
Answer
Answer (as printed): A
Explanation
For first year, S.I. = C.I. Now, ₹ 16 is the S.I. on S.I. for 1 year. ₹ 10 is S.I. on ₹ 100. $$\therefore ₹ 16 \text { is S.I. on } ₹\left(\frac{100}{10} \times 16\right)=₹ 160 \text {. }$$ So, S.I. on principal for 1 year at 10\% is ₹ 160. $$\text { ∴ } \text { Principal }=₹\left(\frac{100 \times 160}{10 \times 1}\right)=₹ 1600 .$$ Amount for 2 years compounded half yearly $$=₹\left[1600 \times\left(1+\frac{5}{100}\right)^{4}\right]=₹ 1944.81 . \therefore \quad \text { C.I. }=₹(1944.81-1600)=₹ 344.81 \text {. }$$ S.I. $=₹\left(\frac{1600 \times 10 \times 2}{100}\right)=₹ 320$. $$\text { ∴ (C.I.) }- \text { (S.I.) }=₹(344.81-320)=₹ 24.81 \text {. }$$
Explanation as extracted from the printed page; notation may be imperfect.