Question

find the amount and the compound interest on rs 5000 for ½ at 14 % per annum compounded half yearly
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Answer 1

Step-by-step explanation:

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

• Principal = Rs. 5000

• Rate % = 14% per annum

• Time = ½ year.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The amount

• Compound interest compounded half- yearly.

$\bf{\underline{\underline\green {Solution:-}}}$

Principal = Rs. 5000

Rate = 14% per annum

For half year rate = 7%

Time = ½ = 1 half year.

As we know that

Amount is given by the formula:-

$\boxed{ \rm \leadsto A = P \bigg(1 + \frac{r}{100} \bigg) ^{n} }$

Here:-

• A = amount = ?

• P = Principal = 5000

• r = rate = 7%

• n = time = 1

Substituting the values:-

${ \rm \implies A = 5000 \bigg(1 + \dfrac{7}{100} \bigg) ^{1} }$

${ \rm \implies A = 5000 \bigg( \dfrac{100 + 7}{100} \bigg) }$

${ \rm \implies A = 5000 \bigg( \dfrac{107}{100} \bigg) }$

${ \rm \implies A = 5000 \times \dfrac{107}{100} }$

${ \rm \implies A = 50 \times {107} }$

${ \rm \implies A = 5350 }$

$\boxed{ \rm \pink{\therefore Amount = Rs.5350 }}$

Now we should find the compound interest

$\boxed{ \rm Compound \: Interest \: Amount - Principal}$

${ \rm \implies5350 - 5000}$

${ \rm \implies350 }$

$\boxed{ \rm \purple{\therefore Compound \: Interest \: = Rs.350}}$

Answer 2

Solution :

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

• Principal, (P) = Rs.5000
• Rate, (R) = 14% p.a
• Time, (n) = 1/2 years

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

As we know that formula of the compounded half-yearly;

$\boxed{\bf{Amount=Principal\bigg(1+\frac{R}{2\times 100} \bigg)^{2n}}}$

A/q

$\mapsto\sf{A=5000\bigg(1+\dfrac{\cancel{14}}{\cancel{2}\times 100} \bigg)^{\cancel{2} \times 1/\cancel{2}}}\\\\\\\mapsto\sf{A=5000\bigg(1+\dfrac{7}{100} \bigg)^{1}}\\\\\\\mapsto\sf{A=5000\bigg(\dfrac{100+7}{100} \bigg)^{1}}\\\\\\\mapsto\sf{A=5000\bigg(\dfrac{107}{100} \bigg)^{1}}\\\\\\\mapsto\sf{A=50\cancel{00} \times \dfrac{107}{\cancel{100} }}\\\\\\\mapsto\sf{A=Rs.(50\times 107)}\\\\\mapsto\bf{A=Rs.5350}$

Now, as we know that compound Interest;

⇒ C.I. = Amount - Principal

⇒ C.I. = Rs.5350 - Rs.5000

⇒ C.I. = Rs.350

Thus;

The amount & compound Interest will be Rs.5350 & Rs.350 .