Mr. Duggal invested Rs. 20000 with rate of interest @ 20% per annum. The interest was compounded half – yearly for the first 1 yr and in the next year it was compounded yearly. What will be the total interest earned at the end of 2 yr?
Solution
Correct Answer: Option B
Principle amount = Rs. 20000
Rate of interest = 20%
Since it is compound interest and it is compounded half-yearly
Rate of interest of half-year = 20/2 = 10%
And in 1 year 2 half years will come.
\(Amount = P \times {\left( {1 + \frac{R}{{100}}} \right)^n}\)
Where, P = Principle amount
R = rate of interest
n = number of years
R = 10% and n =2
∴ Amount after the first year = 20000 × (1 + 0.1)2
⇒ Amount = 20000 × (1.1)2
⇒ Amount = 20000 × 1.21
⇒ Amount = 24200
Rate of interest for next one year = 20%
New Principle amount = 24200
∴ Amount after 2nd year \(= 24200 \times {\left( {1 + \frac{{20}}{{100}}} \right)^1}\)
⇒ Amount = 24200 × (1.2)
⇒ Amount = 29040
∴ Total interest = 29040 – 20000 = 9040
∴ Total interest for 2 years = Rs. 9040
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