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Mathematics

When interest is compounded half-yearly then the formula for C.I. for the given time is :

2 years :

  1. P(1+r100)2PP\Big(1 + \dfrac{r}{100}\Big)^2 - P

  2. P(1+r200)2PP\Big(1 + \dfrac{r}{200}\Big)^2 - P

  3. P(1+r200)4PP\Big(1 + \dfrac{r}{200}\Big)^4 - P

  4. P(1+r100)4PP\Big(1 + \dfrac{r}{100}\Big)^4 - P

Compound Interest

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Answer

When interest is compounded half-yearly.

A = P(1+r2×100)n×2P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{n \times 2}

C.I. = A - P

C.I.=P(1+r2×100)2×2P=P(1+r200)4PC.I. = P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{2 \times 2} - P \\[1em] = P\Big(1 + \dfrac{r}{200}\Big)^4 - P

Hence, Option 3 is the correct option.

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