Multiple choice

A leading financial company in California intends to invest \$100 000 in two types of bonds 'X' and 'Y' at the annual interest rate of 5% and 6% per annum. How much amount should the company invest in the two types of bonds separately to get an interest of \$5 400 from the two bonds?

  1. X: $40,000, Y: $60,000
  2. X: $50,000, Y: $50,000
  3. X: $30 000, Y: $70 000
  4. X: $60 000, Y: $40 000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the amount in bond X and (100,000 - x) be the amount in bond Y. 0.05x + 0.06(100,000 - x) = 5,400. 0.05x + 6,000 - 0.06x = 5,400. -0.01x = -600. x = 60,000. So X = 60,000 and Y = 40,000.

AI explanation

Let X and Y be the amounts invested, so X + Y = 100000. The total interest equation is 0.05X + 0.06Y = 5400. Multiplying the first equation by 0.05 gives 0.05X + 0.05Y = 5000, and subtracting this from the interest equation gives 0.01Y = 400. Solving this shows Y = 40000, which means X = 60000. The company should invest \$60,000 in X and \$40,000 in Y.

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