Question

Find the amount and the compound interest on 18000 for 1 year at 10% per annum, compounded
half-yearly​

Answer 1

Given:

• Principal = Rs. 18,000
• Rate = 10% = $\dfrac{10}{2}$ = 5%
• Time = 1 year = 2 × 1 = years

What To Find:

Amount and Compund Interest.

Formula Used:

$\sf{A = P \left( 1 + \dfrac{R}{100} \right) ^T}$

CI = A - P

Solution:

• Finding the amount

Using the formula,

⇒ $\sf{A = P \left( 1 + \dfrac{R}{100} \right) ^T}$

Substitute the value,

⇒ $\sf{A = 18000 \left( 1 + \dfrac{5}{100} \right) ^2}$

Solve the brackets,

⇒ $\sf{A = 18000 \left( \dfrac{105}{100} \right) ^2}$

Remove the brackets,

⇒ $\sf{A = 18000 \times \dfrac{105}{100} \times \dfrac{105}{100}}$

Cancel the zeros,

$\sf{A = 18 \times 105 \times \dfrac{105}{10}}$

Multiply 18, 105 and 105,

⇒ $\sf{A = \dfrac{1,98,450}{10}}$

Divide 1.98,450 by 10,

⇒ A = Rs. 19,845

• Finding the compound interest

Using the formula,

⇒ CI = A - P

Substitute the values,

⇒ CI = Rs. 19,845 - Rs. 18,000

Subtract the amount,

⇒ CI = 1,845

∴ Therefore, the amount is Rs. 19,845 and compund interest is Rs. 1,845.