Question

Suppose a​ ten-year, $ 1 000 bond with an 8.2 % coupon rate and​ semi-annual coupons is trading for a price of $ 1 034.76. a. What is the​ bond's yield to maturity​ (expressed as an APR with​ semi-annual compounding)? b. If the​ bond's yield to maturity changes to 9.3 % APR​, what will the​ bond's price​ be? a. The​ bond's yield to maturity is nothing​%. ​ (Enter your response as a percent rounded to two decimal​ places.) b. The new price for the bond is ​$ nothing. ​(Round to the nearest​ cent.)

Answer 1

Information provided:

Par value= future value= $1,000

Time= 10 years*2= 20 semi-annual compounding

Coupon rate= 8.2%/2= 4.1%

Coupon payment= 0.041*1,000= $41

Current price= present value= $1,034.76

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

N= 20

PMT= 41

PV= -1,034.76

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 3.8477.

Therefore, the yield to maturity= 3.8477%*2= 7.6953% 7.70%

b.The price of the bond is computed by calculating the present value of the bond.

The present value is computed by entering the below in a financial calculator:

FV= 1,000

N= 20

PMT= 41

I/Y= 9.30%/2= 4.65%

Press the CPT key and PV to calculate the present value.

The value obtained is 929.38.

Therefore, the price of the bond is $929.38.

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