The compound interest on a sum of ₹ 4000 becomes ₹ 630.50 in 9 months. Find the rate of interest, if interest is compounded quarterly.

Given, P =₹ 4000,
n = 9 months = 3/4 yr and
CI = ₹ 630.50
Amount = P + CI = 4000 + 630.50 = ₹ 4630.50
According to the formula,
⇒ Amount = P[(1+R/(100 x 4)]⁴ⁿ
⇒ 4630.50 = 4000(1+R/400)^{4 x 3/4}
⇒ 4630.50 = 4000[(400 + R)/400]³
⇒ 4630.50/4000 = [(400 + R)/400]³
⇒ 9261/8000 = [(400 + R)/400]³
⇒ (21/20)³ = [(400 + R)/400]³
⇒ [(400 + R)/400]/400 = 21/20
⇒ 400 + R = 21 x 20 = 420
∴ R = 420 - 400 = 20%