Zuckain corp. has issued a 10-year coupon bond. the bond is issued at an annual coupon rate of 14%. the face value of the bond is $1,500, and the bond is currently trading at $1,232.56. calculate the bond’s yield to maturity.?

The bond's yield to maturity is 17.96%.

In this question, we need to find the discount rate that equates the periodic interest payment from the bond and the final amount received at maturity upon redemption of the bond.

We can approach this question by assuming two different yield rates and interpolating to arrive at the exact yield to maturity.

Since the current market price of the bond is less than its face value, and given the inverse relationship between bond prices and it's yield, we can conclude that the current yields are above the 14% coupon rate. (When yields and coupon rate are equal, the current market price of the bond and its face value are equal).

We use the bond formula to arrive at the interpolated values:

Bond Price = (C/(1+i)) + (C/(1+i)²) + (C/(1+i)^n) + (MV/(1+i)^n)

where,

C= Coupon Values

i = yield to maturity

MV = Maturity Value.

Substituting values from the question in the above equation, we get,

Bond Price = (210/(1+i)) + (210/(1+i)²) + (210/(1+i)^10) + (1500/(1+i)^10)

We can find the bond price by using 17% in the place of 'i'. When we substitute like this, we get a price of $1290.36.

When we use 18% in the place 'i' in the equation above, we get, 1230.35.

Using these values we can interpolate the yield to maturity as follows:

17 + (1232.56 - 1290.36)/(1290.36-1230.35)

= 17 + (-57.80)/(-60.01)

= 17+ 0.963252

=17.96%

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