Your client, Brooke, decides to start saving for her son's college tuition. Her son was born today and will go to college at age 18 for four years. Brooke wants to save until her son's first year of college. Given the following information, what is the present value of the total amount that Brooke needs to have saved at the beginning of her son's first year of college?

Current tuition: $15,000
Tuition inflation: 6.5%
Brooke's investment return: 10%

a. $29,202
b. $39,010
c. $34,090
d. $31,959

The present value of the total amount that Brooke needs to have saved at the beginning of her son's first year of college is 31.959,13

Explanation:

Tuition Fees after inflation at

Year 18 = 15000* ( 1+6.5%)18 = 46599.8157

Year 19 = 15000* ( 1+6.5%)19 = 49628.8037

Year 20 = 15000* ( 1+6.5%)20 =  52854.6759

Year 21 = 15000* ( 1+6.5%)21 =  56290.2299

Since discount rate = 10%

So discount factor = 1+r = 1+10% = 1.1

Since fees are paid at beginning of period hence

Present Value of Fees = Fees (year 18)/1.1^18 +Fees at Year 19/1.1^19 +Fees at Year 20/1.1^20 + Fees at year 21/1.1^21 = 46599.8157/1.1^18 +  49628.8037/1.1^19 +  52854.6759/1,1^20 + 56290.2299^21 = 31959

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.

d,