Question

The formula for computing compound interest for a principal P that is invested at an annual rate r and compounded annually is given by A = P(1 + r)n , where A is the accumulated amount in the account after n years.
Let’s try a different approach. Substitute the value of 2 for n and solve this formula for r. Verify that you get the following result:
r = PA −1 (Hint: First solve for (1 + r)2 and then take the square root of both sides of the equation.) Notice that you now have a radical expression to work with. Substitute
$5000 for P and $5600 for A (which is the principal plus $600 in interest) to see what your rate must be. Round your answer to the nearest percent.

Answer 1

9514 1404 393

Answer:

• r ≈ 6%

Step-by-step explanation:

Solving for r when n=2, we have ...

  $A=P(1+r)^2\\\\\dfrac{A}{P}=(1+r)^2\\\\\sqrt{\dfrac{A}{P}}=1+r\\\\\boxed{r=\sqrt{\dfrac{A}{P}}-1}$

For the given values of A and P, the value of r is ...

  $r=\sqrt{\dfrac{5600}{5000}}-1=\sqrt{1.12}-1\approx 1.0583-1\\\\\boxed{r\approx 6\%}$