Question

Suppose a​ ten-year, $ 1 comma 000 bond with an 8.4 % coupon rate and semiannual coupons is trading for $ 1 comma 035.37. a. What is the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding)? b. If the​ bond's yield to maturity changes to 9.7 % ​APR, what will be the​ bond's price?

Answer 1

a. $7.88%

b. $917.96

Step-by-step explanation:

The computation is shown below:

a. For computing the yield to maturity we use the RATE formula which is to be shown in the attachment below:

Provided that,

Present value = $1,035.37

Future value or Face value = $1,000

PMT = 1,000 × 8.4% ÷ 2 = $42

NPER = 10 years × 2 = 20 years

The formula is shown below:

= Rate(NPER;PMT;-PV;FV;type)

The present value come in negative

So, after applying the above formula, the yield to maturity is

= 3.94% × 2

= 7.88%

b. Now if the yield to maturity changes to 9.7 % ​APR,

So for computing the bond price we need to apply the Present value formula i.e to be shown in the attachment below:

Given that,

Future value = $1,000

Rate of interest = 9.7% ÷ 2 = 4.85%

NPER = 10 years × 2 = 20 years

PMT = $1,000 × 8.4% ÷ 2 = $42

The formula is shown below:

= -PV(Rate;NPER;PMT;FV;type)

So, after applying the above formula, the price of the bond is $917.96