The difference between simple interest and compound interest on a sum for 2 years at 8% is Rs.16...

Question

The difference between simple interest and compound interest on a sum for 2 years at 8%, when the interest is compounded annually is Rs.16. If the interest were compounded half yearly, then what would be the difference between simple interest and compound interest for the same sum in 2 years?

Answer 1

the difference between the compound interest and simple interest for 2 yearsmay be arrived in the form PxRXR/10000.
R=8,solving get P=2500
Simple interest for the amount=400
comp interest =416
comp interest half-yearly =424.65
hence difference =24.65

Answer 2

the sum is:
16/(1.08*1.08-1.16)=2500

the difference between simple and half yearly interest:
2500(1.04^4-1.16)=25

Answer 3

solution is o.k. The explanation is as under when r=0.08
p*(1.08^2-1.16)=16 gives p=2500 when compounded yearly and when compounded half yearly difference in interest is 2500*(1.04^4-1.16) that comes Rs. 24.6464 say Rs 24.65