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 Rs 16. If the interest were compounded half-yearly, the difference in two interests would be (a) Rs 24.81 (b) Rs 26.90 (c) Rs 31.61 (d) Rs 32.40

Options

A. ₹24.81
B. ₹26.9
C. ₹31.61
D. ₹32.4

Answer

A

Explanation

For first year , S.I. = C.I.
Now , ₹ , 10 is S.I. On ₹ 100 .
₹ 16 is S.I.on ` ₹ ( 100/10 xx 16) = ₹ 160`
So, S.I. on principal for 1 year at 10% is ₹ 60
Principal = ` ₹( 100/10 xx 16) = ₹ 160`
Amount for 2 years compounded half yearly .
`₹[ 1600xx (1+ 5/100)^(4)] = ₹ 1944.81`
C.I. =₹ ( 1944.81 - 1600) = ₹ 344.81
S.I.` = ₹ ((1600 xx 10 xx2)/100) = ₹ 320`
( C.I) - (S.I) = ₹ ( 344.81 -320) = ₹ 24.81 `