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Compound Interest — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsCompound Interest5 Marks
Question
Find the difference between the simple interest and compound interest on 2,500 for 2 years at 4% p.a., compound interest being reckoned semi-annualy.
✓

Answer

P = ₹ 2,500
r = 4% p.a. $=\frac{4}{2}$ = 2% half yearly
T = 2 year = 4 half years

$A = P \left(1+\frac{r}{100}\right)^n$
= ₹ 2,500 $\left(1+\frac{2}{100}\right)^4$
= ₹ 2,500 $\left(1+\frac{1}{50}\right)^4$
= ₹ 2,500 $\left(\frac{51}{50}\right)^4$
= ₹ $\frac{2,500 \times 51 \times 51 \times 51 \times 51}{50 \times 50 \times 50 \times 50}$
= ₹ $\frac{51 \times 51 \times 51 \times 51}{50 \times 50}$
= ₹ $\frac{2,601 \times 2,601}{2,500}$
= ₹ $\frac{67,65,201}{2,500}$
= ₹ 2,706.08

C.I. = A - P
= ₹ (2,706·08 - ₹ 2,500)
= ₹ 206.08
and S.I. = $\frac{ PRT }{100}$ = ₹ $\frac{2,500 \times 4 \times 2}{100}=$ ₹ 200

Difference between C.I. and S.I.
= C.I. - S.I.
= ₹ 206·08 - ₹ 200
= ₹ 6.08

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