Question

find the difference between compound interest on ₹8000 for 3/2 years at 10% pa. when compounded annually and semi annually.

Answer 1

Answer:

• Difference between compound interest on ₹8000 for 3/2 years at 10% p.c.p.a, when compounded annually and semi annually is ₹21.

Step-by-step explanation:

Given that:

• Principal =  ₹8000
• Rate = 10% per annum
• Time = 3/2 years

To Find:

• Difference between compound interest when compounded annually and semi-annually.

Finding interest if it is compounded annually:

Converting Time to mixed fraction:

$\sf{\circ\;Time=\dfrac{3}{2}=1\dfrac{1}{2}\;years}$

As we know that:

• When interest is compounded annually but time is give in fraction.

$\sf{i.e.\;Time=a\dfrac{b}{c}}$

$\sf{Amount=Principal\left(1+\dfrac{Rate}{100}\right)^a\times\left(1+\dfrac{\dfrac{b}{c}\times Rate}{100}\right)}$

Substituting the values,

$\sf{Amount=8000\left(1+\dfrac{10}{100}\right)^1\times\left(1+\dfrac{\dfrac{1}{2}\times 10}{100}\right)}$

$\sf{=8000\times\left(1+\dfrac{10}{100}\right)\times\left(1+\dfrac{5}{100}\right)}$

$\sf{=8000\times\left(\dfrac{100+10}{100}\right)\times\left(\dfrac{100+5}{100}\right)}$

$\sf{=8000\times\dfrac{110}{100}\times\dfrac{105}{100}}$

$\sf{=8\!\!\!\not{0}\!\!\!\not{0}\!\!\!\not{0}\times\dfrac{110}{1\!\!\!\not{0}\!\!\!\not{0}}\times\dfrac{105}{10\!\!\!\not{0}}}$

$\sf{=8\times110\times\dfrac{105}{10}}$

$\sf{=\dfrac{92400}{10}}$

$\sf{=9240}$

Hence,

• Amount is ₹9240 if compounded annually.

Now,

Compound Interest = Amount - Principal

= ₹(9240 - 8000)

= ₹1240

Finding interest if it is compounded semi-annually:

As we know that:

• If interest is compounded semi-annually. Then, Rate = R/2, Time = 2n and:

$\sf{Amount=Principal\left(1+\dfrac{Rate}{100}\right)^{Time}}$

So now,

• Rate = R/2 = 10/2 = 5%
• Time = 2n = 2 × 3/2 = 3 half-years

Substituting the values,

$\sf{Amount=8000\left(1+\dfrac{5}{100}\right)^{3}}$

$\sf{=8000\left(\dfrac{100+5}{100}\right)^{3}}$

$\sf{=8000\left(\dfrac{105}{100}\right)^{3}}$

$\sf{=8000\left(1.05\right)^{3}}$

$\sf{=8000\times1.157625}$

$\sf{=9261}$

Hence,

• Amount is ₹9261 if compounded semi-annually.

Now,

Compound Interest = Amount - Principal

= ₹(9261 - 8000)

= ₹1261

Finding difference between the interests:

Difference = ₹(1261 - 1240)

= ₹21

Therefore,

• There is a difference of ₹21.

Answer 2

Answer:

Rs. 61

Step-by-step explanation:

given

p = Rs8000

T = 3\2 years

R = 10%

find C. I annually.= ?

C.I =?

and different between S. I and C. I =?

we know,

C. I = p[(1+R\100) ^T-1]

= 8000[(1+10\100) ^3\2-1]

=8000[1.15368973-1]

= 8000[0.15368973]

=Rs.1,229.51784

Again,

semi- C. I = p[(1+R\200) ^2T-1]

= 8000[(1+10\200) ^2×3\2-1]

=8000[(1+10\200) ^3-1]

= 8000[1.157625-1]

= 8000×0.157625

= Rs. 1261

different of the interest= annually C. I - semi-C. I

= Rs.1,229.51784 - Rs. 1261

= Rs 31.48216