A $100,000 bond was issued on 1/1/10. It pays interest (coupon) of 6% per annum, with payments occurring every six months. The bond is due in 2 years. A potential investor wanted to know what the bond should be worth on the day of issue, if the prevailing rate for similar bonds (market rate) was 8%. An inexperienced accountant attempted to calculate what the bond should be worth on 1/1/10. Review the work of the accountant, and answer the questions below pertaining to possible mistakes.

Calculation of present value by inexperienced accountant (payment) Periods of interest Interest factor PV 4000 1.0300 3,883 4000 1.0609 3,770 4000 3 1.0927 3,661 4000 1.1255 3,554 100000 2 1.0609 94,260 TOTAL $109,128 24.
The calculation in the PV Column for the first payment
A. Is correct
B. Should be 2,885
C. Should be 2,912
D. Should be 3,846

The correct option is B, should be 2,885

Explanation:

The coupon interest payable  semi-annually is $100,000*6%*6/12=$3000

Using the discount factor formula =1/(1+r)^n where the r is the prevailing interest of 8%/2 since interest is payable in six-month interval

1/(1+4%)=0.961538462

Hence the present value of the first coupon is=0.961538462 *3000=$2885

Hence the correct option is B, the present value of the first payment of coupon should be $2,885.

Hence the inexperienced computation of $3883 is wrong

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.

im confused need to go into details plz thx