Question

Find the difference between the compound interest on Rs 25000 at 16% per annum for six months compounded half-yearly and quarterly respectively. Which option is better?

Answer 1

HEY DEAR ... ✌️

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Here's , ur answer :-


Given Principal = P = Rs. 25000 R = 16% p.a Time = n = 6 month= 1/2 year

for half year compounding CI1 = P{(1+R/200)2n -1} = 25000 * {( 1+16/200)2*1/2 -1}

or CI1= 25000*{(1+2/25)-1} = 25000*{(27/25)-1} = 25000*2/25 = 2000

Similarily for compounding quarterly CI2= P{(1+R/400)4n-1} = 25000 * {( 1+16/400)4*1/2-1}

or CI2= 25000 * {( 1+1/25)2-1} = = 25000 * {( 26/25)2-1} = = 25000 * (262-252)/252

or CI2 = 25000 * (676 -625)/625 = 40*51 = 2040

CI2-CI1 = 2040-2000 = Rs 40/- (Ans)


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Answer 2

Given:

Principle ( P ) = Rs 25000

Rate ( R ) = 16 percent

Time ( N ) = 6 months

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To find : Compound interest for half yearly
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Solution :

Rate = 16 / 2 = 8 percent

Time = 6 * 2 = 12 months
= 1 year

Now,

A = P ( 1 + R / 100 ) to the power N

ie 25000 ( 1 + 8 / 100 ) to power 1
= 25000 * 108
= 27,00,000 .............. ( Amount )

Hence,
CI = A - P

= 27,00,000 - 25000

= 26,75,000 .................( CI for half yearly )
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To find : CI compounded quarterly
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Solution :

R = 16 * 4 = 64

N = 6 months * 4 = 24 months
= 2 years

Now,
A = P ( 1 + R / 100 ) to the power N

= 25000 ( 1 + 64 / 100 ) to the power 2

= 25000 * 164 * 164

= 5,51,400 ................... ( Amount )

Hence,

CI = A - P

= 5,51,400 - 25000

= 5,26,400 Rs ............... ( CI compounded quarterly )

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To find : Difference between CI compounded half yearly and CI compounded quarterly

Solution :

CI half yearly = Rs 26,75,000

CI quarterly = Rs 5,26,400
Now,

26,75,000 - 5,26,000

= 21,49,000 Rs

Since,

26,75,000 > 5,26,400

We can conclude that CI compounded quarterly is a better option

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HOPE THIS HELPS

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