Question

A bond with an annual coupon rate of 6.5%, maturing in 10 years at a value of $1,000 and a current market price of $899.35, will have a yield to maturity (using the approximation formula) of:

Answer 1

To calculate the yield to maturity of the bond, subtract the market price from the face value, divide the result by the market price, and multiply by the number of years until maturity.

Step-by-step explanation:

To calculate the yield to maturity of a bond, you can use the approximation formula. Here are the steps:

• Subtract the current market price of the bond from the face value of the bond.
• Divide the result from step 1 by the market price of the bond.
• Multiply the result from step 2 by the number of years until maturity.

Let's apply this to the given bond:

Subtract $899.35 (market price) from $1,000 (face value): $1,000 - $899.35 = $100.65

Divide $100.65 by $899.35: $100.65 / $899.35 = 0.11195

Multiply 0.11195 by 10 (years until maturity): 0.11195 * 10 = 1.1195

The yield to maturity of the bond is approximately 1.1195 or 111.95%.

Answer 2

The approximate yield to maturity (YTM) for the bond with an annual coupon rate of 6.5% and a current market price of $899.35 can be calculated by dividing the average annual return by the average price, which is equal to 1.74%.

Step-by-step explanation:

To estimate the yield to maturity (YTM) on a bond using the approximation formula, you can follow these steps. First, calculate the annual coupon payment by multiplying the bond's face value by its coupon rate. In this case, for a bond with a 6.5% coupon rate and a face value of $1,000, the annual coupon payment is $1,000 * 0.065 = $65. Next, find the average annual return by adding the bond's face value at maturity to the yearly coupon payment, subtract the current market price, and then divide by the number of years to maturity. Here, it will be ($1,000 + $65 - $899.35) / 10 = $16.565. Finally, calculate the average price by adding the current market price to the face value and dividing by two. For this bond, it will be ($899.35 + $1,000) / 2 = $949.675.

The approximate YTM can be found by dividing the average annual return by the average price: $16.565 / $949.675 = 0.0174 or 1.74%. This rate would need to be compared against the actual YTM calculated with the precise formula or financial calculator, as the approximation may not provide exact results.