What is the yield to maturity of a bond purchased for $898.90 with a $1,000 par value, 10% coupon rate, and 8 years to maturity?

To calculate the yield to maturity (YTM) of the bond, we need to understand that YTM represents the total return anticipated on a bond if it is held until maturity. It accounts for all cash flows, including coupon payments and the difference between purchase price and par value.

In this case, the bond has a par value of $1,000, a 10% coupon rate, and is purchased for $898.90. This means the bond pays $100 annually (10% of $1,000). Over the 8 years until maturity, the investor will receive:

• Annual coupon payments: $100 per year for 8 years = $800
• At maturity, the bondholder will also receive the par value of $1,000.

Therefore, the total cash flows received will be:

• Total cash flow = $800 (from coupons) + $1,000 (at maturity) = $1,800

Since the bond is purchased at a discount ($898.90), the investor also gains from the difference between the purchase price and the par value when the bond matures.

To determine the YTM, one can use a financial calculator or spreadsheet software to solve the following equation:

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