Question

find the difference in compound interest on rs 6000for 1 year at rate of 4%per annum if in the first case interest is paid half yearly and in the second case quarterly.

Answer 1

6000×104/100×6/12 =3120
principal amt for 6 months
6000/2=3000
3120-3000=120 for 1st case
6000×104/100×3/12=1560
principal amt for 3 months
6000×3÷12= 1500
1560-1500=60 for second case

Answer 2

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Here is your answer
For the first case Compounded half yearly
P = 6000
T = 1 year
n = 2
R = 4% p.a
= 4/2 % half yearly
= 2%
Now
A = P(1+R/100)^n
$= 6000 \times (1 + \frac{2}{100} ) {}^{2} \\ = 6000 \times ( \frac{50 + 1}{50} ) {}^{2} \\ = 6000 \times ( \frac{51 \times 51}{50 \times 50} )\\ = 6242.40$
So CI = 6242.40 - 6000
= 242.40

NOW
For second case Compounded quarterly
P = 6000
T = 1 years
n = 4
R = 4%p.a
= 4/4% quarterly
= 1%
Now
A =P(1+R/100)^n
$= 6000 \times (1 + \frac{1}{100} ) {}^{4} \\ = 6000 \times ( \frac{101}{100} ) {}^{4} \\ = \frac{6000 \times 101 \times 101 \times 101 \times 101}{100 \times 100 \times 100 \times 100 } \\ = 6243.62$
CI = 6243.62 - 6000
= 243.62

The difference between them is
= 243.62 - 242.40
= Rs 1.22

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