Question

find the compound interest on Rs 1000 at 8 percent p.a. for 1 integer 1/2 years when the interest is compounded half yearly.​

Answer 1

Question :

Find the compound interest on Rs 1000 at 8 percent p.a. for 1 and ½ years when the interest is compounded half yearly.

To Find :

The Compound Interest.

We Know :

$\bullet$ Amount formula :

(Compounded Semi - Annually)

$\:\:\:\:\:\:\:\:\:\blue{\sf{\underline{\boxed{A = P\left(1 + \dfrac{R}{200}\right)^{2n}}}}}$

Where,

• A = Amount
• P = Principal
• R = Rate of interest p.a.
• n = Time period

$\bullet$ Compound Interest = Amount - Principal

Solution :

Given :

• Principal = ₹ 1000

• Rate = 8 %

• Time = 1½ years = 3/2 years

To Find the Amount yield :

Using the Amount Formula and Substituting the values in it ,we get :

$\:\:\:\:\:\:\:\:\:\purple{\sf{A = P\left(1 + \dfrac{R}{200}\right)^{2n}}} \\ \\ \\ \\ \implies \sf{A = 1000\left(1 + \dfrac{8}{200}\right)^{2 \times \dfrac{3}{2}}} \\ \\ \\ \\ \implies \sf{A = 1000\left(\dfrac{200 + 8}{200}\right)^{\not{2} \times \dfrac{3}{\not{2}}}} \\ \\ \\ \\ \implies \sf{A = 1000\left(\dfrac{208}{200}\right)^{3}} \\ \\ \\ \\ \implies \sf{A = 1000\left(\dfrac{104}{100}\right)^{3}} \\ \\ \\ \\ \implies \sf{A = 1000\left(\dfrac{52}{50}\right)^{3}} \\ \\ \\ \\ \implies \sf{A = 1000\left(\dfrac{26}{25}\right)^{3}}$

$\implies \sf{A = 1000 \times \dfrac{26}{25} \times \dfrac{26}{25} \times \dfrac{26}{25}} \\ \\ \\ \\ \implies \sf{A = 1000 \times \dfrac{26}{25} \times \dfrac{26}{25} \times \dfrac{26}{25}} \\ \\ \\ \\ \implies \sf{A = 40 \times 26 \times \dfrac{26}{25} \times \dfrac{26}{25}} \\ \\ \\ \\ \implies \sf{A = 8 \times 26 \times \dfrac{26}{25} \times \dfrac{26}{5}} \\ \\ \\ \\ \implies \sf{A = \dfrac{8 \times 26 \times 26}{5 \times 25}} \\ \\ \\ \\ \implies \sf{A = \dfrac{140608}{125}} \\ \\ \\ \\ \implies \sf{A = 1124.86(approx.)} \\ \\ \\ \\ \therefore \purple{\sf{A = 1124.86}}$

Hence , the Amount yield is ₹ 1124.86.

Compound Interest :

We Know that ,

CI = Amount - Principal

• Amount = ₹ 1124.86

• Principal = ₹ 1000

Substituting the values in the for Formula ,we get :

==> CI = ₹ (1124.86 - 1000)

==> CI = ₹ 124.86

Hence , the Compound Interest is ₹ 124.86

Additional information :

• Simple Interest = $\bf{\dfrac{P \times R \times t}{100}}$

• Principal = $\bf{\dfrac{100 \times SI}{R \times t}}$

• Rate = $\bf{\dfrac{100 \times SI}{P \times t}}$

• Time = $\bf{\dfrac{100 \times SI}{R \times P}}$