You buy a bond for $976 that has a coupon rate of 7% and a maturity of 5-years. A year later, the bond price is $1,136.

You buy a bond for $976 that has a coupon rate of 7% and a maturity of 5-years. A year later, the bond price is $1,136. (Assume a face value of $1,000 and annual coupon payments.)
a. What is the new yield to maturity on the bond?


b. What is your rate of return over the year?



Explanation

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.

Bond price	=	PV of coupon payments + PV of face value
Bond price	=	C × ((1 / r) – {1 / [r(1 + r)t]}) + FV / (1 + r)t
$1,136	=	(0.07 × $1,000) × ((1 / r) – {1 / [r(1 + r)(5 – 1)]}) + $1,000 / (1 + r)(5 – 1)
	=	0.0368, or 3.68%

To solve for r, use trial-and-error, a financial calculator, or a computer. See the calculator solution below.

b.

Rate of return	=	[Annual interest + (Ending price – Beginning price)] / Beginning price
	=	($74 + 1,136 – 976) / $976
	=	0.2398, or 23.98%

Calculator computations:

Enter

5 – 1

–1,136

74

1,000

N

I/Y

PV

PMT

FV

Solve for

3.68