# Consider a 10-year bond with a 3.6% coupon rate

## What is the bond’s quarterly YTM and APR?

Given a 10-year bond with a 3.6% coupon rate, $1,000 face value, and quarterly coupon payments trading for $930.10, what are the bond's quarterly Yield to Maturity (YTM) and Annual Percentage Rate (APR)?

(a) 4.47% and 1.49%

(b) 1.97% and 1.97%

(c) 1.61% and 3.22%

(d) 1.117% and 4.47%

## Answer:

The bond's quarterly Yield to Maturity (YTM) is 1.117% and its Annual Percentage Rate (APR) is 4.47%.

The bond's Yield to Maturity (YTM) can be calculated by trial and error method to find the interest rate that matches the market price. The bond pricing formula for a bond with periodic coupon payments is:

Bond price = [C * (1 - (1 + r/n) ** (-n*t)) / (r/n) + FV / ((1 + r/n) ** (n*t))],

Where:
**C** = Total annual coupon payment ($36 in this case)
**FV** = Face value ($1,000)
**r** = Yield to Maturity (YTM)
**n** = Number of periods per year (4 for quarterly payments)
**t** = Time to maturity in years (10)

Given the bond's price of $930.10, solving this equation yields a quarterly YTM of approximately 1.117%, which can be converted to an APR of 4.47%.

Therefore, the correct choice is (d) 1.117% and 4.47% for the bond's quarterly YTM and APR, respectively.