Calculate, to the nearest cent, the present value of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time. HINT [See Quick Example 4.] 5 years, at 1.2% per year, compounded weekly (52 times per year)

$941.77  

Explanation:

The formula for present value when interest is compounded on a weekly basis is shown below:

PV=FV/(1+r/t)^(nt)

FV=future cash flow=$1000

r=interest rate=1.2%

t=number of times interest is compounded yearly=52

n=number of years prior to receiving the future amount=5 years

PV=1000/(1+1.2%/52)^(5*52)

PV=1000/(1+0.000230769 )^260

PV=1000/(1.000230769)^260

PV=$941.77  

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.

answer; foreign exchange transaction;