4. The prices of discount bonds (all with maturity value of $1,000) maturing in years 1, 2, 3, 4, 5 are given below. Price Time to Maturity 920 1 860 2 790 3 700 4 600 5 What is the yield to maturity on a risk-free 5% bond due in 5 years (also with maturity value of $1,000)

YTM = 10.5%

Explanation:

Solution

Given that:

The cash flow related  with the 5% bond are computed below:

t =  0     1 (50) 2 (50) 3(50) 4 (50) 5(1050)

Now,

We calculate the discount factors which is given below:

1 /1 + r₁ = 920/1000 = 0.92

1/(1 + r₂)² = 860/1000 = 0.86

1/(1 + r₃)³ = 790/1000 = 0.79

1/(1 + r₄)⁴ = 700/1000 = 0.7

1/(1 + r₅)⁵ = 600/1000 0.6

Thus,

P₅% bond = 50 (0.92) + 50 (0.86) + 50 (0.79) + 50 (0.7) +1050 (0.6)

=$793. 50

For the yield  to maturity (YTM) is refereed to as the IRR of this bond.

Now to solve for the YTM we have teh following.

P₅% bond = 50/YTM ║ 1- 1/(1 +YTM)⁵║ + 1000/(1+ YTM)⁵

793.5 = 50/YTM ║ 1- 1/(1 +YTM)⁵║ + 1000/(1+ YTM)⁵

Therefore

YTM = 10.5%

Note:  the present value of all coupons was computed by applying the annuity formula, also added the PV of the face value

answer: b. false

the staff is a set of five horizontal lines and four spaces which represent a different musical pitch. the lines and the spaces are numbered from bottom to top, the bottom line is the first line and the fifth line is the line on the top. the notes on the top of the staff (fifth line) have a higher pitch than a note at the bottom of the staff.