Multiple choice

A man invested two equal sums of money, one at 10% per annum, interest compounded half-yearly and the second part at a certain percent, interest compounded annually. If he gets equal amounts after 3 years, what is the rate of interest on second investment?

  1. 9.75%

  2. 10%

  3. 10.75%

  4. 10.25%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the first investment at 10% compounded half-yearly, the effective rate is (1 + 0.10/2)² - 1 = 0.1025 or 10.25% annually. After 3 years, the amount is P(1.1025)³. For the second investment at rate r compounded annually, the amount is P(1+r)³. Since amounts are equal: (1.1025)³ = (1+r)³, giving r = 0.1075 or 10.75%.

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