Multiple choice

The ratio of two amounts is 4 : 5. If they are lent out at compound interest for 2 years and 1 year respectively, then the equal amount is received. Find the rate of interest per annum.

  1. 20%

  2. 30%

  3. 25%

  4. 21%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let amounts be 4x and 5x. Using compound interest formula A = P(1 + r/100)^t: 4x(1 + r/100)² = 5x(1 + r/100). Cancel x and (1 + r/100): 4(1 + r/100) = 5, so 1 + r/100 = 5/4 = 1.25. Therefore r/100 = 0.25 and r = 25%. Verify: 4(1.25)² = 4(1.5625) = 6.25, and 5(1.25) = 6.25. Equal amounts received.

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