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A sum lent at compound interest amounts to 72.8% more than itself in 3 years, interest compound annually at a certain rate percent per annum. What will be the compound interest on a sum of Rs.9,000 for \(1\frac{1}{2}\)years at the same rate, if the interest is compound six-monthly?
1. Rs.2,979
2. Rs.2,997
3. Rs.2,977
4. Rs.2,799

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Best answer
Correct Answer - Option 1 : Rs.2,979

Given:

Sum amounts to 72.8% more than itself in 3 years,

When Compounded annually.

Formula Used:

A = P + CI

A = P(1 + R/100)n

Where, 

CI is compound interest,

A is amount,

P is principle,

R is rate, 

n is total number of years

Calculation:

Let the sum be Rs. 1,000

Amount to 72.8% more in 3 years

Amount = CI + P

⇒ Amount = (72.8/100) × 1,000 + 1,000

⇒ Amount = 728 + 1,000

⇒ Amount = 1,728

Now putting the value in the formula,

⇒ 1,728 = 1,000(1 + R/100)3

⇒ 1,728/1,000 = {(100 + R)/100}3

⇒ (12/10)3 = {(100 + R)/100}3

⇒ 12/10 = (100 + R)/100

⇒ 120 = 100 + R

⇒ R = 120 – 100

⇒ R = 20%

Now compounding Rs.9,000 for 3/2 years at the same rate,

If the interest is compound six-monthly,

For 3/2 years,

⇒ 3/2 × 12

⇒ 18 months

But compounded six-monthly,

⇒ 18/6 = 3

When compounded half-yearly, i.e. six-monthly,

⇒ R = 20/2 = 10%

Now using formula,

⇒ A = 9,000(1 + 10/100)3

⇒ A = 9,000(11/10)3

⇒ A = 9,000 × 11/10 × 11/10 × 11/10

⇒ A = 9 × 11 × 11 × 11

⇒ A = 11,979

Now for compound interest,

⇒ CI = A – P

⇒ CI = 11,979 – 9,000

⇒ CI = 2,979

∴ The compound interest is Rs. 2,979.

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