Bowie, age 52, has come to you for help in planning his retirement. He works for a bank, where he earns $60,000. Bowie would like to retire at age 62. He has consistently earned 8% on his investments and inflation has averaged 3%. Assuming he is expected to live until age 95 and he has a wage replacement ratio of 80%, how much will Bowie need to have accumulated as of the day he retires to adequately provide for his retirement lifestyle?

Bowie will require  saving for $1,101,832.05 to achieve their goal.

Explanation:

He expect to have wages 800% of what he currently owns:

60,000 x 80% = 48,000

Now, this will increase 3% per year for inflation reasons:

Principal48,000.00

time10.00

rate0.03000

Amount64,507.99

Now, we solve for the present value of an annuity of 33 year (95 - 62) with a real rate according to Irwin method of:

1.08/1.03 - 1 = 0.048543

C64,507.99

time33

rate0.048543

PV$1,101,832.0536

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.

match each type of restriction with one of its effects.

a. land-use laws

b. labor laws

c. banking regulations

a. controlled development of towns and cities

b. protection of young workers

c. greater financial stability