Assume an investor with 5 years investment horizon is considering purchasing a 7 years 6% coupon selling at par. The investor expects to reinvest the coupon at 5% and that the bond will be selling to offer a yield to maturity of 4% in five years. What is the expect total return for this bond? Express your answer on a bond-equilent basis and on an effective annual rate basis.

To calculate the expected total return on the bond, we need to consider both the coupon payments and the capital gain or loss upon maturity. Let's break down the steps to get the answer.

Step 1: Calculate the total coupon payments received over the investment horizon.
The bond has a 7-year maturity, and the coupon rate is 6%. The investor will hold the bond for 5 years. Each year, the investor will receive a coupon payment equal to 6% of the par value (selling at par means the bond's price is equal to its face value).

Coupon payment per year = 6% * Par value

Step 2: Calculate the future value of the reinvested coupon payments.
The investor plans to reinvest the coupon payments at a 5% interest rate. We need to calculate the future value (FV) of the coupon payments after 5 years.

FV of reinvested coupons = Coupon payment per year * (1 + Reinvestment rate)^Number of years

Step 3: Calculate the capital gain or loss upon maturity.
The bond is expected to be selling at a yield to maturity (YTM) of 4% in 5 years. Since the bond is selling at par currently, the capital gain or loss will be the difference between the face value and the price at which it is selling in 5 years.

Capital gain/loss = Par value - Price in 5 years

Step 4: Calculate the total return.
The expected total return on the bond is the sum of the reinvested coupon payments and the capital gain or loss, divided by the initial investment.

Total return = (FV of reinvested coupons + Capital gain/loss) / Initial investment

Now, let's plug in the numbers and calculate the total return on a bond-equivalent basis and an effective annual rate basis.

Example calculation:
Par value = $1,000
Coupon rate = 6%
Reinvestment rate = 5%
YTM after 5 years = 4%

Step 1: Coupon payment per year = 6% * $1,000 = $60

Step 2: FV of reinvested coupons = $60 * (1 + 5%)^5 = $60 * 1.27628

Step 3: Capital gain/loss = $1,000 - Price in 5 years (unknown)

Step 4: Total return = (FV of reinvested coupons + Capital gain/loss) / Initial investment

Unfortunately, we don't know the price of the bond in 5 years, so we cannot proceed to calculate the total return at this point.