Question

find the difference between the compound interest on ₹ 25,00 at 16% p.a. for 6 months compounded half-yearly and quaterly respectively ,which options is better?

Answer 1

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)

Answer 2

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