What return do you expect earn if you buy the 3 years ,10% coupon bond today and sell it in exactly 1 year( if current price is 1051.45 rupees)

8.02%

Explanation:

Since corporate bonds pay coupons semiannually, it would be important to first all determine the semiannual yield to maturity of this bond using a financial calculator as shown below:

We need to set the calculator to its end mode before making the following inputs:

N=6(number of semiannual coupons in 3 years=3*2=6)

PMT=50(semiannual coupon=face value*coupon rate/2=1000*10%/2=50)

PV=-1051.45 (current price)

FV=1000(bond's face value)

CPT

I/Y=4.02%

After one year, there would 4 semiannual coupons left, we can compute the bond price as shown thus:

N=4

PMT=50

I/Y=4.02(without % sign)

FV=1000

CPT

PV=1,035.56

The expected rate of return over one year is computed thus:

N=2(number of semiannual coupons in 1 year holding period)

PMT=50(the amount of each semiannual coupon)

PV= -1051.45

FV=1,035.56(selling price after one year)

CPT=4.01%(on a semiannual basis)

annual rate of return=4.01%*2=8.02%

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.