Suppose an investor plans to invest a given sum of money.She can earn an effective annual rate of 5% on Security A,while Security B will provide an effective annual rate of 12%.Within 11 years' time,the compounded value of Security B will be more than twice the compounded value of Security A.(Ignore risk,and assume that compounding occurs annually.)

Question

Quizplus · Accepted Answer

Let's assume the given sum of money is $100.

After 11 years, the compounded value of Security A will be:
$100(1+0.05)^{11}\approx $163.86

After 11 years, the compounded value of Security B will be:
$100(1+0.12)^{11}\approx $310.58

Since the question states that the compounded value of Security B will be more than twice the compounded value of Security A, we can set up the following inequality:

$310.58 > 2\cdot $163.86

Simplifying the inequality, we get:

$310.58 > $327.72

Since this inequality is true, we can conclude that Security B will provide more compounded value than twice the compounded value of Security A, making the given statement true.

Suppose an Investor Plans to Invest a Given Sum of Money.She