Question

A $1,500 bond that has a coupon rate of 4.30% payable semi-annually and maturity of 5 years was purchased when the yield was 2.80% compounded semi-annually. What was the book value of the bond after 6 payments?

Answer 1

The book value of the bond after 6 payments is $1,705.12.

Step-by-step explanation:

To calculate the book value of the bond after 6 payments, we need to use the present value formula. The present value formula is used to determine the current worth of future cash flows. In this case, the bond pays coupon payments semi-annually, so we will calculate the present value of each coupon payment and the present value of the bond's face value.

First, we need to calculate the semi-annual coupon payment. The coupon rate is given as 4.30% and the face value of the bond is $1,500. So, the semi-annual coupon payment would be 4.30% x $1,500 / 2 = $32.25.

To determine the present value of the bond's cash flows, we will use the present value formula. The formula is PV = C / (1+r)^n, where PV is the present value, C is the cash flow, r is the discount rate, and n is the number of periods.

In this case, the discount rate is the yield of 2.80% compounded semi-annually. So, the discount rate per period would be 2.80% / 2 = 1.40%. The number of periods would be 6 payments, which is equal to 6 periods.

Now, we can calculate the present value of each cash flow. The present value of the coupon payments would be:

1. $32.25 / (1 + 1.40%)^1 = $31.83
2. $32.25 / (1 + 1.40%)^2 = $31.43
3. $32.25 / (1 + 1.40%)^3 = $31.03
4. $32.25 / (1 + 1.40%)^4 = $30.63
5. $32.25 / (1 + 1.40%)^5 = $30.24
6. $32.25 / (1 + 1.40%)^6 = $29.87

The present value of the bond's face value would be:

$1,500 / (1 + 1.40%)^6 = $1,460.09

Finally, we can calculate the book value of the bond after 6 payments by adding up the present value of the coupon payments and the present value of the face value:

$31.83 + $31.43 + $31.03 + $30.63 + $30.24 + $29.87 + $1,460.09 = $1,705.12