You have just received notification that you have won the $2.15 million first prize in the centennial lottery. however, the prize will be awarded on your 100th birthday (assuming you’re around to collect), 65 years from now. what is the present value of your windfall if the appropriate discount rate is 12 percent? (do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to 2 decimal places, e. g., 1,234,567.89.)

The present value is $1359.24

Explanation:

Giving the following information:

You have just received notification that you have won the $2.15 million first prize in the Centennial Lottery.

You will receive the price 65 years from now. The interest rate is 12%.

We need to use the following formula:

PV= FV/(1+i)^n

PV= 2150000/(1.12^65)= 1359.24

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.