A sum of money of Rs. 64000 yield a compound interest of Rs. 10088 in 9 months, find rate of interest p.a. if interest is compounded quarterly.

20%

Amount = 64000 + 10088 = 74088

⇒ Amount = P (1 + \(\frac{R}{100}\))^t

⇒ 74088 = 64000 (1 + \(\frac{R}{100}\))³

⇒ \(\frac{74088}{64000}\) = (1 + \(\frac{R}{100}\))³         

⇒ (\(\frac{21}{20}\))³ = (1 + \(\frac{R}{100}\))³

⇒ (\(\frac{21}{20}\)) = (1 + \(\frac{R}{100}\))

⇒ R = \(\frac{1}{20}\) = 5% (quarterly)

⇒ Rate p.a. = 5% × 4 = 20%