Question

find the amount and compound interest on 12000 for 2 years at the rate of 20% per annum ,when the interest is compounded semi annually

Answer 1

Solution :

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

• Principal, (P) = Rs.12000
• Time, (n) = 2 years
• Rate, (R) = 20% p. a.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The amount and compound Interest.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Formula use : (Semi-annual)

$\bf{\boxed{\bf{A=P\bigg(1+\frac{R}{100} \bigg)^{2*2} }}}}}$

$\mapsto\sf{A=12000\bigg(1+\cancel{\dfrac{10}{100}}\bigg)^{4} }\\\\\\\mapsto\sf{A=12000\bigg(1+\dfrac{1}{10} \bigg)^{4} }\\\\\\\mapsto\sf{A=12000\bigg(\dfrac{10+1}{10} \bigg)^{4} }\\\\\\\mapsto\sf{A=12000*\dfrac{11}{10} *\dfrac{11}{10} *\dfrac{11}{10} *\dfrac{11}{10} }\\\\\\\mapsto\sf{A=12\cancel{000}*\cancel{\dfrac{14641}{10\cancel{000}}} }\\\\\\\mapsto\sf{A=12*\dfrac{14641}{10} }\\\\\\\mapsto\sf{A=Rs.(12\times 1464.1)}\\\\\\\mapsto\sf{\pink{A=Rs.17569.2}}$

∴ The amount of the Interest is Rs.17569.2.

&

$\leadsto\sf{Compound\:Interest\:(C.I.)=A-P}\\\\\leadsto\sf{C.I.=Rs.(17569.2-12000)}\\\\\leadsto\sf{\pink{C.I.=Rs.5569.2}}$

∴ The C.I of the Interest is Rs.5569.2.

Answer 2

Answer:

Given:

• Compound interest on 12000 for 2 years at the rate of 20% per annum, when the interest is compounded semi annually.

Find:

•Find the required amount.

According to the question:

• 12000 = Compound interest for 2 years.

• 20 % = Rate per annum.

• Interest is compound semi-anually.

Know terms:

• (A) = Amount.

• (P) = Principal.

• (R) = Rate%.

• (n) = number of years (n4).

Using formula:

A = P (1 + R/100)^2 × 2

Calculations:

⇒ A = 12000 (1 + 10/100)^4

⇒ A = 12000 (1 + 1/5)^4

⇒ A = 12000 [(5 + 1)/5]^4

⇒ A = 12000 × 11/5 × 11/5 × 11/5 × 11/5

⇒ A = [12000 × 14641/10000]

⇒ A = [12 × 14641 ] = 17569.2

⇒ A = 17569.2

So, 24883.2 is the amount of interest:

Using formula:

⇒ CI = A - P

⇒ CI = [175692 - 12000]

⇒ CI = 5569.2

Therefore, 5569.2 is answer.