A debt of $3571.31 is due November 1, 2025. What is the value of obligation on May 1, 2016, if money is worth 4% compounded semi-annually? The is the value of the obligation is $.

  2500.49

Step-by-step explanation:

  --Given--

    Amount (A): $3571.31

           Rate (r): 4%

Compound (n): 2                          **semi-annually means 2 times a year**

           Time (t): 9                          **2016 to 2025 is 9 years time**

  --Solve--

     P = A / (1 + r/n)^nt

         = 3571.31 / (1 + .04/2)^(2 * 9)

         = 3571.31 / (1.02 )^(18)

         = 3571.31 / 1.02¹⁸

         = 3571.31 / 1.02¹⁸

         = 3571.31 / 1.428246

         = 2500.49

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°