The difference between the compound and the simple interest on a sum for 2 years at 10% per annum, when the interest is compounded annually, is Rs. 28. If the yearly interest were compounded half-yearly, the difference in the two interests will be :
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When interest compounded annually
2 years CI Rate %
10+1010×10100=21 %
2 years SI Rate % = 10+10 = 20 %
According to the question.
(21−20) % of sum = Rs.28
Sum =281×100 = Rs. 2800
When interest is compounded half-yearly
Rate %=102=5 %
Time = 2×2 = 4
Effective Rate % of CI for 2 half yearly
=5+5+5×5100= 10.25%
Effective Rate % of CI for 4 half year
=10.25+10.25+10.25×10.25100
= 20.50 + 1.050625 = 21.55 %
Effective Rate % of SI for 4 years
= 5×4 = 20 %
Difference in Rate % = (21.55−20) = 1.55%
Required difference
=1.55100×2800=43.4
Hence Required difference=Rs.43.4
HOPE IT HELPS ✌
2 years CI Rate %
10+1010×10100=21 %
2 years SI Rate % = 10+10 = 20 %
According to the question.
(21−20) % of sum = Rs.28
Sum =281×100 = Rs. 2800
When interest is compounded half-yearly
Rate %=102=5 %
Time = 2×2 = 4
Effective Rate % of CI for 2 half yearly
=5+5+5×5100= 10.25%
Effective Rate % of CI for 4 half year
=10.25+10.25+10.25×10.25100
= 20.50 + 1.050625 = 21.55 %
Effective Rate % of SI for 4 years
= 5×4 = 20 %
Difference in Rate % = (21.55−20) = 1.55%
Required difference
=1.55100×2800=43.4
Hence Required difference=Rs.43.4
HOPE IT HELPS ✌
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