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Question:

A person borrowed a sum of ₹30800 at 10% p.a. for 3 years, interest compounded annually. At the end of two years, he paid a sum of ₹13268. At the end of 3rd year, he paid ₹ x to clear of the debt. What is the value of x ?

Explanation:

Amount to be paid after 2 years = 30800${\left(1+\frac{10}{100}\right)}^2$

= 30800${\left(\frac{11}{10}\right)}^2$

= 30800$\left(\frac{121}{100}\right)$

= ₹37268

Amount paid by the person = ₹13268

Remaining amount = ₹37268 - ₹13268 = ₹24000

Amount to be paid at the end of 3rd year to clear debt(i.e, compound interest on ₹24000 for next 1 year) = 24000${\left(1+\frac{10}{100}\right)}^1$

⇒ x = 24000$\left(\frac{11}{10}\right)$

⇒ x = ₹26400

Hence, the correct answer is Option A