Question

Question 49

ch 13 You purchase a $1000 bond for $875. It pays $80 a year (i.e.,
the semiannual coupon is 4 percent), and the bond matures after ten
years. What is the yield to maturity?
(Hint: you are solving for I/YR. Don't forget to set your financial
calculator accordingly for P/YR and adjust N accordingly.)
10.75%
10%
9.5%
5 pts
10.5%

Answer 1

The yield to maturity of the bond is 10.5%.

To calculate the yield to maturity (YTM) of the bond:

1. Identify the variables:

Face Value (FV) = $1,000

Purchase Price (PV) = $875

Coupon Payment (PMT) = $80 (semi-annual)

Number of Years to Maturity (N) = 10 years

Number of Coupon Payments per Year (P/YR) = 2 (semi-annual)

2. Set up the formula:

The formula for YTM is:

YTM = PMT * [(1 - (1 + I/YR)^(-N * P/YR)) / (I/YR)] + (FV - PV) / (N * P/YR)

3. Substitute the values:

YTM = 80 * [(1 - (1 + I/YR)^(-10 * 2)) / (I/YR)] + (1000 - 875) / (10 * 2)

4. Solve for YTM using a financial calculator:

Set P/YR to 2 (semi-annual)

Set N to 20 (total number of coupon payments)

Set PV to -875 (negative because it represents an outflow)

Set PMT to 80

Set FV to 1000

Solve for I/YR (YTM)

5. Calculate the YTM:

Using a financial calculator, we get the YTM as:

YTM = 10.5%

Therefore, the yield to maturity of the bond is 10.5%.