The difference of compound interest (in ₹) on | vedclass

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(A) When compounded half-yearly:Here,$P = 800, R = 20 \%, t = 1$ year.Since it is compounded half-yearly,the rate $R' = 20/2 = 10 \%$ and time $n = 1

Vedclass · Accepted Answer

$4.40$

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(A) When compounded half-yearly:Here,$P = 800, R = 20 \%, t = 1$ year.Since it is compounded half-yearly,the rate $R' = 20/2 = 10 \%$ and time $n = 1 	imes 2 = 2$ half-years.$CI = P[(1 + R'/100)^n - 1] = 800[(1 + 10/100)^2 - 1] = 800[(1.1)^2 - 1] = 800[1.21 - 1] = 800 	imes 0.21 = ₹ 168$.When compounded quarterly:Here,$P = 800, R = 20 \%, t = 1$ year.Since it is compounded quarterly,the rate $R'' = 20/4 = 5 \%$ and time $n = 1 	imes 4 = 4$ quarters.$CI = P[(1 + R''/100)^n - 1] = 800[(1 + 5/100)^4 - 1] = 800[(1.05)^4 - 1]$.$(1.05)^4 = 1.21550625$.$CI = 800[1.21550625 - 1] = 800 	imes 0.21550625 = ₹ 172.405$.Difference $= ₹ 172.405 - ₹ 168 = ₹ 4.405 \approx ₹ 4.40$.

The difference of compound interest (in ₹) on ₹ $800$ for $1$ year at $20 \%$ per annum when compounded half-yearly and quarterly is:

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