Two people save money in a tax-deferred individual retirement account that earns 8% annually. person a invests $ 3,000 a year from age 20 to 29, but then never saves another penny. person b starts investing $ 3,000 a year at age 30 and saves that same amount annually for the rest of his life. who has more money in the account at age 65?

Person B

Explanation:

If Person A begins investing $3,000 a year from age 20 to 29 he would have invested a total of $30,000. Each year he earns 8% of the amount in his account, so the first year he earns $3,000 x 8% = $240, the second year $6,000 x 8 = $ 480...and so on. Total interest earned are $99,600 from the age of 20 thru 65, because at age 30 no more money in invested but the $30,000 continues to earn 8% interest until the age of 65.

Person A earns a total of $30,000 + $99,600 =  $129,600

Person B begins investing $3,000 a year at age 30 and invests a total of $108,00 from age 30 thru 65. Interest of 8% also needs to be considered from age 30 thru age 65. Total interest earned is $159,840.

Person B earns a total of $108,000 + $159,840 = $267,840

So Person B would earn more money at the age of 65.

PS: Spreadsheet attached.

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.

hi noah!

the first time you break a rule, you get a warning.

if you continue to break rules you get kicked out for a certain amount of time.

so, to answer your question 1.

hope this buddy!

- courtney