You just won a lottery - congratulations! your parents have always told you to plan for the future, so since you already have a well- paying job you decide to invest rather than spend your lottery winnings. the payment schedule from the lottery commission is $100,000 after taxes at end of year one and 19 more payments of exactly $100,000 after taxes in equal annual end- of- the- year deposits (i. e., the first of the next 19 deposits is one year from today) into your account pays 7% compounded annually. how much money will be in your account after the last deposit is made?

$2,027,087.791

Explanation:

Given that,

Lottery commission = $100,000

Remaining 19 payments annually = $100,000

Compounded payment = 7%

Total compounded payment till end:

Where,

A0 = Compounded payment at first deposit = $7,000

t = Total time in years = 20 years

n = No. of compounding periods per year = 1

r = Nominal annual interest rate expressed as a decimal = 0.07

Therefore,

               = 7,000 × 3.8696

               = $27,087.79

After 20 years,

Total amount deposited will be = $20,00,000 + $27087.79

                                                     = $2,027,087.791

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.

the answer is account d