We need to calculate the yield to maturity (YTM) of a bond given its current price, coupon rate, par value, and time to maturity. The bond has a current price of $908, a coupon rate of 11%, a par value of $1000, and 8 years to maturity. We need to find the YTM to the nearest percent.

Applied MathematicsFinanceBondsYield to MaturityFinancial MathematicsApproximation
2025/7/8

1. Problem Description

We need to calculate the yield to maturity (YTM) of a bond given its current price, coupon rate, par value, and time to maturity. The bond has a current price of 908,acouponrateof11908, a coupon rate of 11%, a par value of 1000, and 8 years to maturity. We need to find the YTM to the nearest percent.

2. Solution Steps

The approximate formula for Yield to Maturity (YTM) is:
YTM=(C+(FVCV)/N)/((FV+CV)/2)YTM = (C + (FV - CV)/N) / ((FV + CV)/2)
Where:
CC = Annual coupon payment
FVFV = Face Value (Par Value)
CVCV = Current Value (Current Price)
NN = Number of years to maturity
First, calculate the annual coupon payment:
C = \text{Coupon Rate} \times \text{Face Value} = 0.11 \times \1000 = \110110
Next, plug the values into the YTM formula:
YTM = (\110 + (\1000 - \908)/8) / ((\1000 + \908)/2)$
YTM = (\110 + \92/8) / (\1908/2)$
YTM = (\110 + \11.5) / \954$
YTM = \121.5 / \954954
YTM=0.127358YTM = 0.127358
Convert the YTM to a percentage and round to the nearest percent:
YTM=0.127358×100%=12.7358%13%YTM = 0.127358 \times 100\% = 12.7358\% \approx 13\%

3. Final Answer

The yield to maturity is approximately 13 percent.
So, the answer is d. 13 percent.

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