An investor purchases a bond with a face value of $1,000 that pays 6 percent annually and was bought for $900. What is the yield to maturity for this bond?

To calculate the yield to maturity (YTM) for the bond, we consider several key factors: the bond's annual coupon payments, the current price of the bond, its face value, and the time remaining until maturity.

The face value of the bond is $1,000, with an annual coupon rate of 6 percent. This means the bond pays $60 annually (6% of $1,000). Since the investor purchased the bond for $900, the YTM can be thought of as the rate of return anticipated if the bond is held until maturity, accounting for both the annual coupon payments and the capital gain realized when the bond matures at its face value.

To arrive at the YTM, the formula involves:

1. Calculating the annual coupon payment, which is $60.
2. Considering the capital gain, which is the difference between the maturity value ($1,000) and the purchase price ($900), equal to $100.
3. Estimating the total return earned over the duration of the bond, expressed as a percentage of the bond's purchase price.

The YTM formula can be approximated by:

YTM ≈ [Coupon Payment + (Face Value - Purchase Price) / Years to M