Question

Find the difference between the compound intrest on ₹25,000 at 16%per annum for six months compounded half-yearly and quaterly respectively. Which option is better?

Answer 1

Given , principal = ₹ 25,000 , rate = 16% per annum ,time = 6 months

=> when the interest is compounded half yearly:

Find the amount 1:
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p = ₹ 25,000,

rate = 16% p.a = 16 / 2 = 8 % half yearly

time = 6 months = 1 half year

Amount = p [ 1 + ( r /100 ) ]^t

amount1 = 25,000 [ 1 + ( 8 / 100 ) ]^1

amount1 = 25,000( 108/ 100 ) = ₹ 27000

Find the C.I :

C.I 1 = amount 1 - principal

C.I 1 = 27000 - 25000 = ₹ 2000

=> when the interest is compounded quarterly:

since 1 quarter = 12 / 4 = 3 months

p = 25,000 , rate = 16 = 16 / 4 = 4 % quarterly

time = 6 months = 2 quarters

Find the amount2 :
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amount2 = p [ 1 + ( r/ 100 ) ]^t

amount2 = 25,000 [1 +( 4 / 100 ) ]^2

amount2 = 25,000×( 52/ 50 )× (52/50 )

amount2 = ₹ 27040

C.I2 = amount2 - principal

C.I2 = ₹ 27040 - 25,000 = ₹ 2040

difference = C.I2 - C.I1 = 2040 - 2000

difference = ₹ 40

therefore , required difference = ₹ 40

Answer : difference = ₹ 40

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