Huang has a goal to have $50,000 in five years for a down payment on a house. He
invests in an annuity paying 6% interest, compounded monthly. How much does he
have to deposit each month to reach his goal? Enter your answer rounded to the
nearest cent. Omit the dollar sign and comma.

$716.64

Step-by-step explanation:

We will use the savings annuity formula

A(t)=d((1+r/n)n⋅t−1)r/n

and solve for d. In this case, A(5)=$50,000, r=0.06, and n=12 compounding periods per year. Substitute these values into the formula.

$50,000=d((1+0.06/12)5⋅12−1)0.06/12.

Simplify and solve for d.

$50,000$50,000 d=d(1.00560−1)0.005=69.7700305 d=$716.64

He will have to deposit $716.64 every month to reach his goal.

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°

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: