The difference between simple interest and compound interest on a sum for 2 years at 8%, when the interest is compounded annually Rs.16. If the interest was compounded half-yearly, the difference in two interests would be nearly :
Rs.16
Rs.16.80
Rs.21.85
Rs.24.64
Explanation:
For 1st year, S.I = C.I
Thus, Rs.16 is the S.I on S.I for 1 year, which at 8% is thus Rs.200
i.e.S.I on the principal for 1 year is Rs.200
Principal = Rs. (100×2008×1)=(100×2008×1)=Rs.2500
Amount for 2 years, compounded half-yearly
=Rs.[2500×(1+4100)4][2500×(1+4100)4]=Rs.2924.64
C.I = Rs.424.64
Also, S.I = Rs.(2500×8×2100)(2500×8×2100)=Rs.400
Hence, [(C.I)-(S.I)] = Rs. (424.64-400)=Rs.24.64
For 1st year, S.I = C.I
Thus, Rs.16 is the S.I on S.I for 1 year, which at 8% is thus Rs.200
i.e.S.I on the principal for 1 year is Rs.200
Principal = Rs. (100×2008×1)=(100×2008×1)=Rs.2500
Amount for 2 years, compounded half-yearly
=Rs.[2500×(1+4100)4][2500×(1+4100)4]=Rs.2924.64
C.I = Rs.424.64
Also, S.I = Rs.(2500×8×2100)(2500×8×2100)=Rs.400
Hence, [(C.I)-(S.I)] = Rs. (424.64-400)=Rs.24.64