A sum of Rs. 1000 is invested for 5 years
at rate of 12% per annum. Find
compound interest and due amount​

Given:

• Principal = Rs. 1000
• Rate = 12 %
• Time = 5 years

What To Find:

We have to find –

• Compound Interest and amount.

Formulas Needed:

[tex]\bf \to A = P \bigg[ 1 + \dfrac{R}{100} \bigg]^{T}[/tex]

[tex]\bf \to CI = A – P[/tex]

Solution:

• Finding the A.

Use the formula,

[tex]\bf \to A = P \bigg[ 1 + \dfrac{R}{100} \bigg]^{T}[/tex]

Substitute the values,

[tex]\bf \to A = 1000 \bigg[ 1 + \dfrac{12}{100} \bigg]^{5}[/tex]

Solve the brackets,

[tex]\bf \to A = 1000 \bigg[ \dfrac{112}{100} \bigg]^{5}[/tex]

Remove the brackets,

[tex]\bf \to A = 1000 \times \dfrac{112}{100} \times \dfrac{112}{100} \times \dfrac{112}{100} \times \dfrac{112}{100} \times \dfrac{112}{100}[/tex]

Solve the fractions,

[tex]\bf \to A = 1000 \times \dfrac{17623416832}{10000000000}[/tex]

Cancel the zeros.

[tex]\bf \to A = \dfrac{17623416832}{10000000}[/tex]

Divide the numbers,

[tex]\bf \to A = Rs. \: 1762.3 – [approx.\!][/tex]

• Finding the CI.

Use the formula,

[tex]\bf \to CI = A – P[/tex]

Substitute the values,

[tex]\bf \to CI = 1762.3 – 1000[/tex]

Subtract the numbers,

[tex]\bf \to CI = Rs. \: 762.3[/tex]

Final Answer:

∴ Thus, the amount is Rs. 1762.3 and the compound interest is Rs. 762.3.