Question

A certain sum under compound interest, interest being compounded annually earns an interest of Rs. 864 and Rs. 1,036.80 respectively in the third year and fourth year. Find the sum

Answer 1

The sum is 3000 and rate of interest is 20% per annum.

Let the sum of money is P and rate of interest per annum is r.

compound interest of 3rd year = compound interest in 3 years - compound interest in 2 years

= [P(1 + r/100)³ - P] - [P(1 + r/100)² - P]

= P(1 + r/100)²(r/100)

so, P(1 + r/100)²(r/100) = 864 ......(1)

similarly, compound interest of 4th year = P(1 + r/100)³(r/100) = 1036.8 ........(2)

dividing equations (1) and (2) we get,

864/1036.8 = 1/(1 + r/100)

⇒1036.8/864 - 1 = r/100

⇒(1036.8 - 864)/864 = r/100

⇒r = 20%

putting r = 20% in equation (1) we get,

P(1 + 20/100)²(20/100) = 864

⇒P(1 + 1/5)²(1/5) = 864

⇒P(36/25)(1/5) = 864

⇒P = 125 × 864/36 = 125 × 24 = 3000

hence the sum is 3000 Rs.