You purchased a 3 year coupon bond one year ago. Its par value is $1,000 and coupon rate is 6%, paid annually. At the time you purchased the bond, its yield to maturity was 6.5%. Suppose you sell the bond after receiving the first interest payment.

What is the total rate of return from holding the bond for the year if the yield to maturity remains at 6.5% when you sell it?

• 5.5%
• 6%
• 6.25%
• 6.5%
• 6.75%

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

Solution: D

The current price of the bond is

[[math]] P_0=\frac{$ 60}{1.065}+\frac{$ 60}{1.065^2}+\frac{$ 1060}{1.065^3}=$ 986.76 [[/math]]

You can sell it in one year for

[[math]] P_1=\frac{$ 60}{1.065}+\frac{$ 1060}{1.065^2}=$ 990.90 [[/math]]

But there is also the [math]$ 60[/math] of coupon. So the total return is

[[math]] R o R=($ 990.90+$ 60) / \$ 986.76-1=6.5 \% [[/math]]

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.