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.