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Question

(B) Let the principal be $P$.Simple Interest $(SI)$ for $2$ years at $10 \%$ per annum:$SI = P 	imes \frac{10 	imes 2}{100} = 0.2P$Compound Interest

Vedclass · Accepted Answer

$8000$

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(B) Let the principal be $P$.Simple Interest $(SI)$ for $2$ years at $10 \%$ per annum:$SI = P 	imes \frac{10 	imes 2}{100} = 0.2P$Compound Interest $(CI)$ for $2$ years compounded half-yearly:Rate $R = 10 \% / 2 = 5 \%$ per half-year.Time $n = 2 	imes 2 = 4$ half-years.$CI = P \left(1 + \frac{5}{100}ight)^4 - P = P \left(1.05^4 - 1ight)$$CI = P (1.21550625 - 1) = 0.21550625P$Difference $= CI - SI = 0.21550625P - 0.2P = 0.01550625P$Given,$0.01550625P = 124.05$$P = \frac{124.05}{0.01550625} = 8000$Thus,the principal is ₹ $8000$.

The difference between the simple interest on a certain sum at the rate of $10 \%$ per annum for $2$ years and compound interest which is compounded every $6$ months is ₹ $124.05$. What is the principal (in ₹)?

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