Using the time value of money Helen wants to take the next four years off work to travel around the world. She estimates her annual cash needs at $31,000 (if she needs more, she will work odd jobs). Helen believes she can invest her savings at 10% until she depletes her funds. Requirements 1. How much money does Helen need now to fund her travels?

$84,693.67

Explanation:

The relevant formula to employ is the present value (PV) formula.

Present value (PV) refers the current value of a future amount cash or stream of cash flows given a certain return rate. To obtain PV, the future cash flow are discounted using the rate of return as the discount rate.

The formula for calculating the PV is given as follows:

PV = FV/(1 + r)^n (1)

Where,

PV = Present Value = ?

r = rate of return or the discount rate = 10% = 0.1

FV = $31,000

n = number of years = 4 years

If we substitute the values given above into equation (1), we will have:

PV = 31,000/(1 + 0.1)^4

     = 31,000/(1.1)^4

     = 31,000/ 1.4641  

PV = $21,173.42  

Since Hellen wants to take the next four years off work to travel around the world, the PV of $21,173.42 will be multiplied by 4 to obtain the amount she needs now as follows:

Amount Needed Now = $21,173.42 × 4

                                     = $84,693.67  

Therefore, Helen needs $84,693.67  now to fund her travels.

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.