Question

Find the compound interest on a sum of ₹ 80000 , at 10 % per annum ,for 18 months , compounded half yearly.

Answer 1

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• ➬ Principle = Rs.80000
• ➬ Rate = 10 %
• ➬ Time = 18 months
• ➬ Compounded half - yearly = 1 year = 2T

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• ➬ Compound Interest = ?

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❒ Formula Used :

$\large{\blue{\bigstar}} \: \: {\underline{\boxed{\red{\sf{C.I = P \bigg[1 + \dfrac{R}{100} \bigg]^T - P}}}}}$

➢Here :

• ➳ C.I = Compound Interest = ?
• ➳ P = Principle = Rs. 80000
• ➳ R = Rate = 10%
• ➳ T = Time = 18 months = 3T

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❒ Finding the Compound interest :

$\qquad{:\implies\sf{C.I = P\bigg[1 + \dfrac{R}{100} \bigg]^T - P}}$

$\qquad{:\implies\sf{C.I = 80000\bigg[1 + \dfrac{10}{100} \bigg]^3 - 80000}}$

$\qquad{:\implies\sf{C.I = 80000\bigg[1 + \cancel\dfrac{10}{100} \bigg]^3 - 80000}}$

$\qquad{:\implies\sf{C.I = 80000\bigg[1 +0.10 \bigg]^3 - 80000}}$

$\qquad{:\implies\sf{C.I = 80000\bigg[1.10 \bigg]^3 - 80000}}$

$\qquad{:\implies\sf{C.I = 80000 \times 1.331 - 80000}}$

$\qquad{:\implies\sf{C.I = 106480 - 80000}}$

$\large\qquad{\qquad{\orange{:\longmapsto{\underline{\boxed{\sf{ C.I = 26480}}}}}}{\pink{\bigstar}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Therefore :

❝ Compounded interest of the given sum is Rs. 26480. ❞

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Answer 2

Information provided with us:

• Sum is of ₹80000 at 10% per annum , for 18 months.

What we have to calculate:

• Compound Interest on that sum of money

Using Formula:

• C.I. = P( 1 + r/100)^n - P

Where,

• C.I. is compound interest
• n is time taken
• P is principal
• r is rate of interest

Required calculations:

We have,

• P is ₹ 80000
• R is 10%

First of all finding out number of months,

We know that,

• 1 year = 12 months

Therefore, 18 months = 1.6 years

But interest is compounded half yearly so n would be 3 half years.

Putting the values in the formula of compound interest,

➺ C.I. = 80000 (1 + 10/100)³ - 80000

➺ C.I. = 80000 (1 + 1/10)³ - 80000

➺ C.I. = 80000 (10+1 / 10)³ - 80000

➺ C.I. = 80000 (11 / 10)³ - 80000

➺ C.I. = 80000 (1.1)³ - 80000

➺ C.I. = 80000 (1.1 × 1.1 × 1.1) - 80000

➺ C.I. = 80000 (1.21 × 1.1) - 80000

➺ C.I. = 80000 (1.331) - 80000

➺ C.I. = 80000 × 1.331 - 80000

➺ C.I. =106,480 - 80000

➺ C.I. = 26,480

Therefore, compound interest is Rs.26,480..!!