Question

You purchased an annual interest coupon bond one year ago that had sixyears remaining to maturity at that time. The coupon interest rate was 10%and the par value was $1,000. At the time you purchased the bond, the yieldto maturity was 8%. If you sold the bond after receiving the first interestpayment and the yield to maturity continued to be 8%, your annual total rateof return on holding the bond for that year would have been Select one: 7.00%. 7.82%. 8.00%. 11.95%. None of the options

Answer 1

Answer:

Your annual total rate of return on holding the bond for that year would have been:

Select one: 8.00%.

Explanation:

If the YTM of the bond does not change during the year, it means that at the time the bond was sold, the total rate of return would be the same as was when the bonds were purchased, in this case 8%.

Bond Value

Principal Present Value  =  F /  (1 + r)^t

Coupon Present Value   =  C x [1 - 1/(1 +r)^t] / r

• Price of the Bond at the moment it was purchased:

The price of this bond it's $630,17 + $462,29 = $1,092.46

Present Value of Bonds $630,17 = $1,000/(1+0,08)^6  

Present Value of Coupons $462,29 =  $100 (Coupon) x 4,62

4,62 =   [1 - 1/(1+0,08)^6 ]/ 0,08

• Price of the Bond one year later:

The price of this bond it's $680,58 + $399,27 = $1,079.85

Present Value of Bonds $680,58 = $1,000/(1+0,08)^5  

Present Value of Coupons $399,27 =  $100 (Coupon) x 3,99

3 ,99 =   [1 - 1/(1+0,08)^5 ]/ 0,08

The buyer of the bond get:

Year 0        Year 1   Year 1       TOTAL  RECEIVED

-$1,092,.6   $100  $1,079.85   $1,179.85

Rate of Return: $1,179.85/$1,092,.6 = 8%