Question

The current price of a bond is $950. It has a face value of $1,000, a maturity date of 2 years and pays a 4% coupon rate every year. Calculate the price if the yield is 5%, and when it is 9%. Use linear interpolation to estimate the correct yield. (Hint: The previous problem solves for the price of the bond with a yield of 5%).

must show all work step by step

Answer 1

Yield = Cash Flow or Coupon Received/Current Market Price

Coupon rate = 4%

=> Coupon received every year = 4% of 1000 = 40

So for a yield of 5%,

CMP = 40/5% = 800

And for a yield of 9%,

CMP = 40/9% = 444.444

So for linear interpolation, we have a linear line as the yield curve, which means the equation of the line will be:

Y = mX + c

where Y = yield and X = current market price

So putting the market price for 5% and 9% yield we get two equations,

5% = 800X + c

9% = 444.444X + c

On solving the equation we get,

X = -0.0112% and C = 0.1396

So for price (X) = 950

yield = 950*(-0.0112%) + 0.1396 = 3.32%

So the answer with linear interpolation is 3.32%