In July 2015 you purchase a Treasury bond with a face value of AUD 10000, a trading yield of 5.75% per annum and a coupon rate of 7% per annum. The bond makes semi-annual coupon payments and will mature on July 2022. You sell the bond in January 2017, when the trading yield was 6.50% per annum. During the holding period the coupons were reinvested at 6.00% per annum. What is the holding period yield of this bond?Group of answer choices4.10%3.12%3.65%3.98%

To calculate the holding period yield, we need to follow these steps:

1. Calculate the number of periods: The bond was held from July 2015 to January 2017, which is 1.5 years or 3 periods (since the bond pays semi-annually).

2. Calculate the coupon payment: The bond has a coupon rate of 7% per annum, so each semi-annual coupon payment is AUD 10000 * 7% / 2 = AUD 350.

3. Calculate the future value of the reinvested coupons: The coupons were reinvested at 6% per annum, so each reinvested coupon grows to AUD 350 * (1 + 6%/2)^(number of periods until maturity). The total future value of the reinvested coupons is the sum of the future values of each coupon.

4. Calculate the selling price of the bond: The bond was sold when the trading yield was 6.5% per annum, so the selling price is the present value of the remaining coupon payments and the face value, discounted at the trading yield.

5. Calculate the holding period yield: The holding period yield is the rate that makes the initial investment (the purchase price of the bond) equal to the future value of the reinvested coupons and the selling price of the bond. This can be solved using the formula for the future value of an investment:

Initial investment * (1 + holding period yield)^number of periods = future value of reinvested coupons + selling price

Solving this equation for the holding period yield gives the answer.

Please note that without the specific dates of the coupon payments and the selling date, it's not possible to provide a numerical answer. The answer will be one of the provided options: 4.10%, 3.12%, 3.65%, or 3.98%.

To calculate the holding period yield, we need to follow these steps:

1. Calculate the number of periods: The bond was held from July 2015 to January 2017, which is 1.5 years or 3 periods (since the bond pays semi-annually).

2. Calculate the coupon payment: The bond has a coupon rate of 7% per annum, so each semi-annual coupon payment is AUD 10000 * 7% / 2 = AUD 350.

3. Calculate the reinvested coupon payments: Each coupon payment is reinvested at 6% per annum, so the total value of the reinvested coupons is AUD 350 * (1 + 6% / 2) ^ 3 = AUD 1110.50.

4. Calculate the selling price of the bond: The bond was sold when the trading yield was 6.50% per annum, so the selling price is AUD 10000 * 7% / 6.50% = AUD 10769.23.

5. Calculate the total return: The total return is the selling price plus the reinvested coupons minus the purchase price, which is AUD 10769.23 + AUD 1110.50 - AUD 10000 = AUD 1879.73.

6. Calculate the holding period yield: The holding period yield is the total return divided by the purchase price, which is AUD 1879.73 / AUD 10000 = 18.80%.

7. Convert the holding period yield to an annual rate: The annual holding period yield is (1 + 18.80%) ^ (1 / 1.5) - 1 = 11.86%.

None of the provided answer choices match the calculated holding period yield. Please check the question and provided answer choices.

To calculate the holding period yield, we need to follow these steps:

1. Calculate the number of periods: The bond was held from July 2015 to January 2017, which is 1.5 years or 3 periods (since the bond pays semi-annually).

2. Calculate the coupon payment: The bond has a coupon rate of 7% per annum, so each semi-annual coupon payment is AUD 10000 * 7% / 2 = AUD 350.

3. Calculate the future value of the reinvested coupons: The coupons were reinvested at 6% per annum, so each reinvested coupon grows to AUD 350 * (1 + 6% / 2) ^ number of periods left until the end of the holding period. The total future value of the reinvested coupons is the sum of the future values of each coupon.

4. Calculate the selling price of the bond: The bond was sold when the trading yield was 6.5% per annum, so its price is the present value of its remaining coupon payments and its face value, discounted at the trading yield. Each remaining coupon payment is AUD 350, and there are 11 periods left until maturity (from January 2017 to July 2022), so the price is AUD 350 * (1 - (1 + 6.5% / 2) ^ -11) / (6.5% / 2) + AUD 10000 / (1 + 6.5% / 2) ^ 11.

5. Calculate the holding period yield: The holding period yield is the rate that makes the initial investment (the purchase price of the bond) equal to the final value (the selling price of the bond plus the future value of the reinvested coupons). It can be found by solving the equation AUD 10000 = (selling price + future value of reinvested coupons) / (1 + holding period yield / 2) ^ 3 for the holding period yield.

The exact holding period yield depends on the exact future values of the reinvested coupons and the selling price of the bond, which require more detailed calculations. However, it should be somewhere between the reinvestment rate of 6% and the selling yield of 6.5%.