Question

You just bought a bond that pays a $35 coupon every six months. The yield on the bond right now is 7.0%, and it matures in five years. How much did you pay?

1) $1,000.00
2) $854.46
3) $1,070.00

Answer 1

To find the price paid for a bond with semi-annual coupon payments, you need to calculate the present value of the annuity of the coupon payments and the present value of the face value, both discounted by the yield, and add them together.

Step-by-step explanation:

To calculate the price of the bond you just bought, we need to discount the future cash flows back to their present value. This includes the coupon payments you receive every six months as well as the face value you will receive at maturity. Given that the bond yields 7.0%, we can use this as the discount rate. Since there are five years to maturity and coupon payments are made semi-annually, we have a total of 10 coupon payments. The coupon payment is $35 every six months.

Using the formula for the present value of an annuity for the coupon payments: PV = C * [(1 - (1 + r)^(-n)) / r] where C is the coupon payment, r is the yield per period, and n is the total number of periods. Additionally, we calculate the present value of the face value, which is discounted back for the number of periods at the given yield.

Let's calculate it step by step:

1. Calculate semi-annual yield: 7.0% annual yield divided by 2, as payments are semi-annual, which equals 3.5% per period.
2. Calculate present value of the coupon payments: $35 * [(1 - (1 + 0.035)^(-10)) / 0.035].
3. Calculate present value of the face value: $1,000 / (1 + 0.035)^10.
4. Sum the present value of the coupon payments and the present value of the face value.

After calculating these values and summing them, you'll find the price you paid for the bond.