An amount is invested in a bank at compound rate of interest

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An amount is invested in a bank at compound rate of interest . The total amount, including interest, after first and third year is ₹ 1200 and ₹ 1587, respectively . What is the rate of interest ?

1. 10 %
2. 3.9 %
3. 12 %
4. 15 %

Correct Option: D

Let amount be ₹ P and rate of interest be R % annually .
According to the question,
Amount after 1st yr = ₹ 1200
⇒ P(1 + R/100) = 1200 ...(i)
Amount after 3rd yr = 1587
⇒ P(1 + R/100)³ = 1587 ...(ii)
On dividing Eq. (ii) from Eq. (i), we get
(1 + R/100)2 = 1587/1200 = 529/400
⇒ 1 + R/100 = 23/20
⇒ R/100 = 3/20
∴ R = 15 %