Question

calculate the amount and compound interest on 6000 in 2½ years at 15 per year​

Answer 1

Answer:

• Amount = ₹8530.125
• Compound Interest = ₹2530.125

Step-by-step explanation:

Given that:

• Principal = ₹6000
• Rate = 15% per annum
• Time = 2½ years

To Find:

• The amount and compound interest.

Solution:

As we know that:

$\sf{\circ\;When\;time\;is\;in\;fraction\;\left(i.e.\;a\dfrac{b}{c}\right). \;\bf{Then,}}$

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

Substituting the values,

$\sf{\longmapsto 6000\left(1+\dfrac{15}{100}\right)^2\times\left(1+\dfrac{\dfrac{1}{2}\times 15}{100}\right)}$

Solving further,

$\sf{\longmapsto 6000\left(\dfrac{100+15}{100}\right)^2\times\left(1+\dfrac{1\times 15}{2\times100}\right)}$

$\sf{\longmapsto 6000\left(\dfrac{115}{100}\right)^2\times\left(1+\dfrac{15}{200}\right)}$

$\sf{\longmapsto 6000\left(\dfrac{115}{100}\right)^2\times\left(\dfrac{200+15}{200}\right)}$

$\sf{\longmapsto 6000\left(\dfrac{115}{100}\right)^2\times\left(\dfrac{215}{200}\right)}$

Opening the brackets,

$\sf{\longmapsto 6000\times\dfrac{115}{100}\times\dfrac{115}{100}\times\dfrac{215}{200}}$

Cutting off the zeros,

$\sf{\longmapsto 6\!\!\!\not{0}\!\!\!\not{0}\!\!\!\not{0}\times\dfrac{115}{1\!\!\!\not{0}\!\!\!\not{0}}\times\dfrac{115}{10\!\!\!\not{0}}\times\dfrac{215}{200}}$

$\sf{\longmapsto 6\times115\times\dfrac{115}{10}\times\dfrac{215}{200}}$

Reducing the numbers,

$\sf{\longmapsto 6\times115\times\dfrac{23}{2}\times\dfrac{43}{40}}$

Multiplying the numbers,

$\sf{\longmapsto \dfrac{6,82,410}{80}}$

Dividing the numbers,

$\sf{\longmapsto 8530.125}$

Hence,

• Amount is ₹8530.125

Now,

As we know that,

• CI = Amount - Principal

= ₹(8530.125 - 6000)

= ₹2530.125

Hence,

• Compound Interest is ₹2530.125