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Mathematics

A certain sum of money (₹ P) is lent for 3123\dfrac{1}{2} years at r% C.I. compounded yearly. The interest accrued will be:

  1. P(1+r100)72−PP \Big(1 + \dfrac{r}{100}\Big)^{\dfrac{7}{2}} - P

  2. P(1+r100)3×(1+r2×100)1−PP\Big(1 + \dfrac{r}{100}\Big)^3 \times \Big(1 + \dfrac{r}{2 \times 100}\Big)^1 - P

  3. P(1+r2×100)72−PP\Big(1 + \dfrac{r}{2 \times 100}\Big)^{\dfrac{7}{2}} - P

  4. P(1+r2×100)7−PP\Big(1 + \dfrac{r}{2 \times 100}\Big)^7 - P

Compound Interest

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Answer

Given, the principal amount = ₹ P, rate of interest r%.

For complete 3 years it will be calculated normally but for half year it will be calculated by taking 1 half year and half rate of interest.

A = P(1+r100)3×(1+r2×100)1P\Big(1 + \dfrac{r}{100}\Big)^3 \times \Big(1 + \dfrac{r}{2 \times 100}\Big)^1

C.I. = A - P

= P(1+r100)3×(1+r2×100)1−PP\Big(1 + \dfrac{r}{100}\Big)^3 \times \Big(1 + \dfrac{r}{2 \times 100}\Big)^1 - P

Hence, option 2 is the correct option.

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