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Mathematics

Find the difference between compound interest and simple interest on ₹ 8000 in 2 years and at 5% per annum.

Compound Interest

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Answer

For S.I. :

Principal = ₹ 8000

Rate = 5%

Time = 2 years

S.I. = 8000×5×2100\dfrac{8000 \times 5 \times 2}{100} = ₹ 800.

For C.I. :

C.I. = A - P

=P(1+r100)n−P=8000×(1+5100)2−8000=8000×(105100)2−8000=8000×(2120)2−8000=8000×441400−8000=8820−8000=₹820.= P\Big(1 + \dfrac{r}{100}\Big)^n - P \\[1em] = 8000 \times \Big(1 + \dfrac{5}{100}\Big)^2 - 8000 \\[1em] = 8000 \times \Big(\dfrac{105}{100}\Big)^2 - 8000 \\[1em] = 8000 \times \Big(\dfrac{21}{20}\Big)^2 - 8000 \\[1em] = 8000 \times \dfrac{441}{400} - 8000 \\[1em] = 8820 - 8000 \\[1em] = ₹ 820.

Difference between C.I. and S.I. = ₹ 820 - ₹ 800 = ₹ 20.

Hence, difference between C.I. and S.I. = ₹ 20.

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