d timeline.
To calculate the price of the bond, we need to discount all future cash flows to present value using the given yield rate of 4.80% compounded semi-annually. The bond has a coupon rate of 4.55% and a face value of $10,000.
Timeline:
February 10, 2025 - Purchase Date
July 01, 2031 - Redemption Date
To calculate the bond price, we need to determine the cash flows from coupons and the principal at redemption.
Coupon Cash Flows:
The bond pays a coupon of 4.55% of the face value semi-annually.
Number of coupon payments = (2031 - 2025) * 2 = 12
Coupon Payment = Coupon Rate * Face Value / 2 = 0.0455 * $10,000 / 2 = $227.50
Principal Cash Flow:
The bond redeems at the face value of $10,000 on July 01, 2031.
Now we can calculate the present value of each cash flow and sum them up to find the bond price.
Step 1: Calculate the discount rate per period
Yield Rate per Period = Yield Rate / 2 = 4.80% / 2 = 2.40%
Step 2: Calculate the present value of each cash flow
Present Value of Coupon Payments = Σ(Coupon Payment / (1 + Yield Rate per Period)^n) for n = 1 to 12
Present Value of Coupon Payments = Σ($227.50 / (1 + 2.40%)^n) for n = 1 to 12
Present Value of Principal = $10,000 / (1 + 2.40%)^14
Step 3: Sum up the present values of cash flows
Bond Price = Present Value of Coupon Payments + Present Value of Principal
The present value calculations need to be done manually, but you can use a financial calculator or spreadsheet software to make it easier.
Once you find the bond price, you can compare it to the market price to determine if it is a good investment.
A $10,000 bond with a coupon rate of 4.55% was redeemable on July 01, 2031. It was purchased on February 10, 2025 when the yield rate was 4.80% compounded semi- annually. Please include a well-labelle
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