If a 4-year bond with a 7% coupon and a 10% yield to maturity is currently worth $904.90, how much will it be worth 1 year from now if interest rates are constant?

The bond will be worth $925.394 1 year from now.

Explanation:

Customarily the amount of payment that is given to the bond holder at maturity is $1,000, this is known as the face value.

The value of a bond can be determined using the expression below;

T=V c+V face value

where;

T=total bond value

V c=present value of coupon payments

V face value=present value of the face value, and

V c=∑{C / (1+r) ^t}

C=future value of coupon payments

r=yield to maturity

t=number of periods

V face value=F / (1+r) ^T

F=face value of the bond

T=time to maturity

In our case;

C=7% of 1,000 = (7/100) * 1,000=$70

r=10%=10/100=0.1

t=years 1, 2 and 3

F=$1,000

T=4 years

replacing;

V c=∑{C / (1+r) ^t}={70 / (1+0.1) ^1}+{70 / (1+0.1) ^2}+{70 / (1+0.1) ^3}=$174.0796

V face value=F / (1+r) ^T={1,000 / (1+0.1) ^3}=$751.315

T=174.0796+751.315=$925.394